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visibility: public
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# Math

**repo:** [rossant/awesome-math](https://github.com/rossant/awesome-math)  
**category:** [[theory|Theory]]
**related:** [[data-science|Data Science]] · [[algorithms|Algorithms]]

---

# Awesome Math [![Awesome](https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg)](https://github.com/sindresorhus/awesome)

A curated list of awesome mathematics resources.

All resources are freely available except those with a 💲 icon.

# Contents

* [Contents](#contents)
* [General Resources](#general-resources)
    * [Learning Platforms](#[learning](/@harrisonqian/awesome/wiki/programming-languages/learning)-platforms)
    * [Learn to Learn](#learn-to-learn)
    * [Youtube Series](#youtube-series)
    * [Tools](#tools)
    * [Questions and Answers](#questions-and-answers)
    * [Encyclopedia](#encyclopedia)
    * [Books](#books)
    * [Magazines](#magazines)
    * [Blogs](#blogs)
    * [Meetings and Conferences](#meetings-and-conferences)
    * [Misc](#misc)
* [Branches of Mathematics](#branches-of-mathematics)
    * [Foundations of Mathematics](#foundations-of-mathematics)
        * [Transition To Pure Rigour Math](#transition-to-pure-rigour-math)
        * [Set Theory](#set-theory)
        * [Logic](#logic)
        * [Category Theory](#category-theory)
        * [Type Theory](#type-theory)
        * [Homotopy Type Theory](#homotopy-type-theory)
        * [Surreal Numbers](#surreal-numbers)
    * [Number Theory](#number-theory)
        * [Algebraic Number Theory](#algebraic-number-theory)
        * [Analytic Number Theory](#analytic-number-theory)
    * [Algebra](#algebra)
        * [Abstract Algebra](#abstract-algebra)
        * [Group Theory](#group-theory)
        * [Linear Algebra](#linear-algebra)
        * [Ring Theory](#ring-theory)
        * [Galois Theory](#galois-theory)
        * [Lie Algebras](#lie-algebras)
    * [Combinatorics](#combinatorics)
        * [Graph Theory](#graph-theory)
    * [Geometry and Topology](#geometry-and-topology)
        * [Differential Geometry](#differential-geometry)
        * [Algebraic Geometry](#algebraic-geometry)
        * [Algebraic Statistics](#algebraic-statistics)
        * [Topology](#topology)
        * [Algebraic Topology](#algebraic-topology)
    * [Analysis](#analysis)
        * [Real Analysis](#real-analysis)
        * [Harmonic Analysis](#harmonic-analysis)
        * [Complex Analysis](#complex-analysis)
        * [Functional Analysis](#functional-analysis)
        * [Measure Theory](#measure-theory)
        * [Ordinary Differential Equations](#ordinary-differential-equations)
        * [Partial Differential Equations](#partial-differential-equations)
        * [Chaos Theory](#chaos-theory)
    * [Probability and Statistics](#probability-and-statistics)
        * [Probability Theory](#probability-theory)
        * [Statistics](#statistics)
        * [Statistical Learning](#statistical-learning)
        * [Stochastic processes](#stochastic-processes)
    * [Numerical Analysis](#numerical-analysis)
    * [Signal processing](#signal-processing)
    * [Mathematics for Computer Science](#mathematics-for-computer-science)
    * [Mathematical Biology](#mathematical-biology)
    * [Mathematical Physics](#mathematical-physics)
* [Students Lecture Notes](#students-lecture-notes)
* [Related [Awesome](/@harrisonqian/awesome/wiki/miscellaneous/awesome) Lists](#related-awesome-lists)
* [License](#license)

# General Resources

## Learning Platforms

* [Khan Academy](https://www.khanacademy.org/math)
* [Coursera](https://www.coursera.org/courses?query=mathematics&languages=en)
* [MIT OpenCourseWare](http://ocw.mit.edu/courses/mathematics/)
* [edX](https://www.edx.org/course/subject/math)
* [Brilliant](https://brilliant.org/courses/#math-foundational)
* [WooTube](https://misterwootube.com/)
* [Mathigon](https://mathigon.org/)
* [Calculus.org](http://calculus.org/)
* [Ximera](https://ximera.osu.edu/) : free interactive mathematics textbooks (Ohio State University)
* [Almost Fun](https://www.almostfun.org/lessons/)
* [Oxford Mathematics](https://www.youtube.com/c/OxfordMathematics)
* [Math Academy](https://mathacademy.com/)
* [Derivative Calculus Solver](https://www.derivativecalculus.com) — A step-by-step differentiation tool focusing on the chain rule and substitution logic.

## Learn to Learn

* [Understanding Mathematics](https://github.com/nelson-brochado/understanding-math)

## Youtube Series

* [Brandon Foltz](https://www.youtube.com/@BrandonFoltz)
* [StatQuest](https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw)
* [3Blue1Brown](https://www.youtube.com/@3blue1brown)
* [NPTEL](https://www.youtube.com/@iit)
* [Numberphile](https://www.youtube.com/@numberphile)
* [PatrickJMT](https://www.youtube.com/@patrickjmt)
* [Professor Leonard](https://www.youtube.com/@ProfessorLeonard)
  * [Precalculus - College Algebra/Trigonometry](https://www.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP)
  * [Calculus 1](https://www.youtube.com/playlist?list=PLF797E961509B4EB5)
  * [Calculus 2](https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-)
  * [Calculus 3](https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7)
  * [Differential Equations](https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_)
  * [To The Point Math](https://www.youtube.com/playlist?list=PLDesaqWTN6ETc1ZwHWijCBcZ2gOvS2tTN)
* [Crash Course](https://www.youtube.com/@crashcourse)
* [Harvard](https://www.youtube.com/@harvard)
* [MIT OpenCourseWare](https://www.youtube.com/@mitocw)
* [Mathologer](https://www.youtube.com/@Mathologer)
* [The Math District](https://www.youtube.com/@TheMathDistrict)
* [Mathematical Monk](https://www.youtube.com/@mathematicalmonk)
* [The Math Sorcerer](https://www.youtube.com/@TheMathSorcerer)

## Tools

* [Symbolab](https://www.symbolab.com/)
* [Desmos](https://www.desmos.com/calculator)
* [Math Words](http://www.mathwords.com/)
* [Wolfram Alpha](http://www.wolframalpha.com/)
* [Maxima](https://maxima.sourceforge.io/)
* [Sympy](https://www.sympy.org/)
* [Sagemath](http://www.sagemath.org/)
* [MathFlow](https://github.com/Nonanti/MathFlow) - C# math expression library with symbolic computation (differentiation, simplification, equation solving)
* [Unit Converter](https://unitconverters.net)
* [GeoGebra](https://www.geogebra.org/?lang=en)
* [Macaulay2](http://www2.macaulay2.com/Macaulay2/)
* [Singular](https://www.singular.uni-kl.de/)
* [GNU Octave](https://www.gnu.org/software/octave/)
* [Magma](http://magma.maths.usyd.edu.au/magma/)
* [Maple](https://www.maplesoft.com/products/Maple/)
* [Matlab](https://www.mathworks.com/products/matlab.html)
* [Wolfram Mathematica](https://www.wolfram.com/mathematica/)
* [Free Math](https://freemathapp.org)
* [xhub](https://chrome.google.com/webstore/detail/xhub/anidddebgkllnnnnjfkmjcaallemhjee)
* [CopyPasteMathjax](https://www.copypastemathjax.com/)
* [Finance calculators](https://www.financecharts.com/pages/5724-retirement-[calculators](/@harrisonqian/awesome/wiki/miscellaneous/calculators)-and-stock-market-tips)
* [Mathcheap](https://mathcheap.xyz)
* [Midpoint Calculator](https://midpointcalculator.co)
* [Quartiles Calculator](https://quartilecalculator.net)
* [Corca Editor](https://corca.io/)
* [RunMat](https://github.com/runmat-org/runmat) - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.
* [Structural Engineering Tools (SEPCO Engineering)](https://github.com/sepcostructural/structural-engineering-tools) - Free online [calculators](/@harrisonqian/awesome/wiki/miscellaneous/calculators) for beam diagrams, Canadian steel section properties, and pressure conversions.

## Questions and Answers

* [Mathematics Stack Exchange](http://math.stackexchange.com/)
* [MathOverflow](http://mathoverflow.net/) - for professional mathematicians

## Encyclopedia

* [Encyclopedia of Mathematics](https://www.encyclopediaofmath.org)
* [Planetmath](http://planetmath.org/)
* [ProofWiki](https://proofwiki.org/wiki/Main_Page)
* [Wolfram Mathworld](http://mathworld.wolfram.com/)
* [The On-Line Encyclopedia of Integer Sequences](https://oeis.org) - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.
* 💲 [The Princeton Companion to Mathematics](https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics) - Timothy Gowers (Professor, Fields medallist), June Barrow-Green (Professor), and Imre Leader (Professor).
* 💲 [Encyclopedia of Distances (4th Edition)](https://link.springer.com/book/10.1007/978-3-662-52844-0) - Michel Marie Deza, Elena Deza.

## Books

* [Calculus: Basic Concepts for High Schools](https://archive.org/details/TarasovCalculus) - L.V. Tarasov
* [Basics of Algebra, Topology, and Differential Calculus](http://www.cis.upenn.edu/~jean/math-basics.pdf) - Jean Gallier (University of Pennsylvania)
* [Multivariable Calculus](http://people.math.gatech.edu/%7Ecain/notes/calculus.html) - G. Cain, J. Herod (Georgia Tech)
* [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf)
* [Online Mathematics Textbooks](https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html)
* [Beginning and Intermediate Algebra](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf)
* [Free Mathematics Books](https://github.com/EbookFoundation/free-programming-books/blob/master/books/free-programming-books-subjects.md#mathematics)
* [Trigonometry](http://www.mecmath.net/trig/trigbook.pdf)
* [Math for Frontend Web Dev](https://www.manning.com/books/math-for-frontend-web-dev)
* [Grokking Statistics](https://www.manning.com/books/grokking-statistics)
* [The Math Behind Artificial Intelligence](https://www.freecodecamp.org/news/the-math-behind-artificial-intelligence-book) - Tiago Capelo Monteiro (freeCodeCamp)

## Magazines

* [Quanta Magazine](https://www.quantamagazine.org/mathematics/) - Features latest research breakthroughs in an accessible style for non-experts.
* [Bulletin of the American Mathematical Society](https://www.ams.org/journals/bull/all_issues.html) - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.
* [Notices of the American Mathematical Society](http://www.ams.org/cgi-bin/notices/amsnotices.pl?article_id=fullissue&article_type=gallery&gallery_type=fullissue) - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.
* [European Mathematical Society Magazine](https://euromathsoc.org/magazine) - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.
* [Mathematics Today by Institute of Mathematics and its Applications](https://ima.org.uk/publications/mathematics-today/) - News, opinions, and articles related to mathematics, so the reader stays updated.
* [Crux Mathematicorum by Canadian Mathematical Society](https://cms.math.ca/publications/crux/) - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions.

## Blogs

* [BetterExplained](https://betterexplained.com/) - Maintained by Kalid Azad
* [ILoveMaths](http://ilovemaths.com/) - For grades 6 thru 12 in K-12 system
* [3blue1brown](https://www.3blue1brown.com/) - Animated Maths
* [Mathsisfun](https://www.mathsisfun.com) simple text lightweight site for students up to highschool
* [MathematicsIsAScience](https://calculus123.com/wiki/Peter_Saveliev) - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)

## Meetings and Conferences

* [MathsJam](https://mathsjam.com/) - monthly local recreational maths/puzzle meetups and an annual gathering in Staffordshire, England
* [Talking Maths in Public](https://talkingmathsinpublic.uk/) - a conference for maths communicators, running every two years, usually in the UK
* [Bridges](https://www.bridgesmathart.org/) - an annual conference on mathematical connections in art, [music](/@harrisonqian/awesome/wiki/media/music), architecture, and culture. The 2025 meeting is in Eindhoven, Netherlands.

## Misc
* [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics)
* [Paul's Online Math Notes](http://tutorial.math.lamar.edu/) - Paul Dawkins (Lamar University)
* [List of electronic textbooks](http://faculty.atu.edu/mfinan/nnotes.html) - Marcel B. Finan (Arkansas Tech University)
* [Topology Atlas](http://at.yorku.ca/topology/)
* [Recreations in Math](http://djm.cc/library/Recreations_in_Mathematics_Licks_edited.pdf) - H. E. Licks (1917)
* [Magic Squares and Cubes](http://djm.cc/library/Magic_Squares_Cubes_Andrews_edited.pdf) - W. S. Andrews (1917)
* [Convex Optimization](https://web.stanford.edu/~boyd/cvxbook/) - Stephen Boyd and Lieven Vandenberghe
* [Fabrice Baudoin's Notes](https://fabricebaudoin.wordpress.com/) - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more.

# Branches of Mathematics

**Content Format** \
📖 Books \
🎥 Videos \
📝 Lecture notes, slides, articles, papers

## Foundations of Mathematics
### Transition To Pure Rigour Math
* 📝 [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon
* 📝 [Book of Proof](https://richardhammack.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/BookOfProof/) - Richard Hammak (Virginia Commonwealth University)
* 📖 [How to Prove It: A Structured Approach (3rd Edition)](https://ia800501.us.archive.org/7/items/how-to-prove-it-a-structured-approach-daniel-j.-velleman/How%20to%20Prove%20It%20A%20Structured%20Approach%20%28Daniel%20J.%20Velleman%29.pdf) - Daniel J. Velleman (Professor).

### Set Theory

* 📝 [Sets, Relations, Functions](http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html) - Ivo Düntsch, Günther Gediga
* 📝 [An Introduction to Set Theory](http://www.math.toronto.edu/weiss/set_theory.pdf) - William A. R. Weiss
* 📝 [Set Theory and Foundations of Mathematics](http://www.settheory.net/) - Sylvain Poirier
* 📝 [Set Theory on the Stanford Encyclopedia of Philosophy](http://plato.stanford.edu/entries/set-theory/)

### Logic

* 📝 [Introduction to Logic](https://pdfs.semanticscholar.org/6967/f52773d9c2ccfc94658657a5761e0f00e95a.pdf) - Michael Genesereth, Eric Kao (Stanford University)
* 📝 [An Introduction to Formal Logic](https://www.fecundity.com/codex/forallx.pdf) - P.D. Magnus (University at Albany)
* 📝 [A Problem Course in Mathematical Logic](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf) - Stefan Bilaniuk (Trent University)
* 📝 [Computability - An introduction to recursive function theory](http://poincare.matf.bg.ac.rs/~zarkom/Book_Math__Cutland_Computability.pdf) - Nigel Cutland (University of Hull)
* 📝 [Language, Proof, and Logic](http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf) - Jon Barwise, John Etchemendy
* 📝 [Mathematical Logic](http://www.mathematik.uni-muenchen.de/~schwicht/lectures/logic/ws03/ml.pdf) - Helmut Schwichtenberg
* 📝 [Mathematical Logic](http://www.personal.psu.edu/t20/notes/logic.pdf) - Stephen G. Simpson (Pennsylvania State University)
* 📝 [Formal Logic](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf) - Miguel Palomino
* 📝 [Predictive Arithmetic](https://web.math.princeton.edu/~nelson/books/pa.pdf) - Edward Nelson
* 📝 [Proofs and Concepts: the fundamentals of abstract mathematics](http://people.uleth.ca/~dave.morris/books/proofs+concepts.html) - Joy Morris, Dave Morris
* 📝 [Mathematical Reasoning: Writing and Proof](https://www.tedsundstrom.com/mathreasoning) - Ted Sundstrom
* 📝 [Logic and Proof](http://leanprover.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/logic_and_proof/) -  Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn
* 📝 [QED - an interactive textbook](https://teorth.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/QED) - Terence Tao
* 📝 [Open Logic Textbook](http://builds.openlogicproject.org/) - collaborative effort, main contributors listed [here](https://openlogicproject.org/people/)

### Category Theory

* 📝 [Introduction to Category Theory and Categorical Logic](http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf) - Thomas Streicher
* 📝 [An Introduction to Category Theory](http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf) - Harold Simmons
* 📝 [Category Theory](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&rep=rep1&type=pdf) - Steve Awodey (Carnegie Mellon University)
* 📝 [Category Theory](http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf) - B. Pareigis
* 📝 [Category Theory for Computing Science](https://web.archive.org/web/20181221233252/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf) - Michael Barr, Charles Wells
* 📝 [Toposes, Triples and Theories](http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf) - Michael Barr, Charles Wells
* 📝 [Abelian Categories](http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html) - Peter Freyd
* 📝 [Categories and Groupoids](http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html) - P. J. Higgins
* 📝 [Basic Concepts of Enriched Category Theory](http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html) - G. M. Kelley
* 📝 [Abstract and Concrete Categories: The Joy of Cats](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html) - Jiri Adamek, Horst Herrlich, George Strecker
* 📝 [Seven Sketches in Compositionality: An Invitation to Applied Category Theory](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) - Brendan Fong and David I. Spivak (MIT)
* 📝 [Category Theory in Context](http://www.math.jhu.edu/~eriehl/context/) - Emily Riehl (John Hopkins University)

### Type Theory
* 📝 [Proofs and Types](http://www.paultaylor.eu/stable/prot.pdf) - Jean-Yves Girard
* 📝 [Intuitionistic Type Theory](https://archive-pml.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf) - Per Martin-Lof
* 📝 [Type Theory and Functional Programming](https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) - Simon Thompson
* 📝 [Programming in Martin-Lof’s Type Theory](http://www.cse.chalmers.se/research/group/logic/book/book.pdf) - Bengt Nordstrom, Kent Petersson, Jan M. Smith

### Homotopy Type Theory

* 📝 [Homotopy Type Theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf)

### Surreal Numbers

* 📝 [Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness](http://www.math.harvard.edu/~knill/teaching/mathe320_2015_fall/blog15/surreal1.pdf) - D. E. Knuth
* 📝 [Surreal Numbers and Games](http://web.mit.edu/sp.268/www/2010/surreal.pdf)
* 📝 [Conway names, the simplicity hierarchy and the surreal number tree](http://www.ohio.edu/people/ehrlich/ConwayNames.pdf) - Philip Ehrlich

## Number Theory

* 📝 [Elementary Number Theory: Primes, Congruences, and Secrets](http://wstein.org/ent/ent.pdf) - William Stein
* 📝 [Elementary Number Theory](http://math.utoledo.edu/~codenth/Spring_13/3200/ENT-books/Elementary_Number_Theory-Clark.pdf) - W. Edwin Clark (University of South Florida)
* 📝 [A Course on Number Theory](http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf) - Peter J. Cameron
* 📝 [A Computational Introduction to Number Theory and Algebra](http://shoup.net/ntb/ntb-v2.pdf) - Victor Shoup
* 📝 [Number Theory: A Contemporary Introduction](http://alpha.math.uga.edu/~pete/4400FULL.pdf) - Pete L. Clark
* 📝 [An Introduction to the Theory of Numbers](http://www.trillia.com/moser-number.html) - Leo Moser
* 📝 [Yet Another Introductory Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz

### Algebraic Number Theory

* 📝 [Introduction to Algebraic Number Theory](https://feog.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/ANT10.pdf) - F. Oggier
* 📝 [Algebraic Number Theory](http://www.jmilne.org/math/CourseNotes/ANT.pdf) - J.S. Milne
* 📝 [Algebraic Number Theory Course Notes](http://people.math.gatech.edu/~mbaker/pdf/ANTBook.pdf) - Matthew Baker (Georgia Tech)
* 📝 [A Course In Algebraic Number Theory](http://www.math.uiuc.edu/~r-ash/ANT.html) - Robert Ash

### Analytic Number Theory

* 📝 [Introduction to Analytic Number Theory](http://www.math.uiuc.edu/~hildebr/ant/main.pdf) - A.J. Hildebrand (University of Illinois)
* 📝 [Elements of Analytic Number Theory](http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf) - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
* 📝 [Analytic Number Theory](http://www.mathematik.uni-muenchen.de/~forster/v/ann/annth_all.pdf) - Otto Forster (LMU Munich)
* 📝 [Analytic Number Theory - Lecture Notes based on Davenport’s book](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf) - Andreas Strömbergsson

## Algebra

* 📝 [A Course in Universal Algebra](http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html) - S. Burris, H.P. Sankappanavar
* 📝 [A Course in Commutative Algebra](https://faculty.math.illinois.edu/~r-ash/ComAlg.html) - Robert Ash
* 📝 [First Course in Algebra](http://djm.cc/library/First_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910)
* 📝 [Second Course in Algebra](http://djm.cc/library/Second_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911)
* 📝 [Algebra: An Elementary Text-Book, Part I](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf) - G. Chrystal (1904)
* 📝 [Algebra: An Elementary Text-Book, Part II](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_II_Chrystal_edited02.pdf) - G. Chrystal (1900)
* 📝 [Understanding Algebra](https://jamesbrennan.org/algebra) - James W. Brennan

### Abstract Algebra

* 📝 [Introduction to Abstract Algebra](https://zodml.org/sites/default/files/Introduction_to_Abstract_Algebra_0.pdf) - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)
* 📝 [Introduction to Modern Algebra](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf) - David Joyce (Clark University)
* 📝 [Algebraic Methods](https://feog.[github](/@harrisonqian/awesome/wiki/development-environment/github).io/AA11.pdf) - F. Oggier
* 📝 [Abstract Algebra : Theory and Applications](http://abstract.ups.edu/download/aata-20150812.pdf) - Thomas W. Judson, Robert A. Beezer (Austin State University)
* 📝 [An Undergraduate Course in Abstract Algebra](http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf) - Robert Howlett
* 📝 [Elements of Abstract and Linear Algebra](http://www.math.miami.edu/~ec/book) - E.H. Connell (University of Miami)
* 📝 [Abstract Algebra: The Basic Graduate Year](http://www.math.uiuc.edu/~r-ash/Algebra.html) - Robert Ash
* 📝 [Abstract Algebra: Harvard Extension (Archived)](https://web.archive.org/web/20150528171650/extension.harvard.edu/open-[learning](/@harrisonqian/awesome/wiki/programming-languages/learning)-initiative/abstract-algebra) - Benedict Gross
* 📝 [Abstract Algebra: Harvard Extension Videos](https://www.youtube.com/playlist?list=PLA58AC5CABC1321A3) - Benedict Gross

### Group Theory

* 📝 [Notes on Group Theory](https://www2.bc.edu/mark-reeder/Groups.pdf) - Mark Reeder
* 📝 [Group Theory](http://www.jmilne.org/math/CourseNotes/GT.pdf) - J.S. Milne
* 📝 [Notes on Finite Group Theory](http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf) - Peter J. Cameron
* 📝 [Group Theory](http://www.cns.gatech.edu/GroupTheory/index.html) - Pedrag Civitanovic

### Linear Algebra

* 📝 [Fundamentals of Linear Algebra](http://www.math.ubc.ca/~carrell/NB.pdf) - James B. Carrell
* 📝 [Linear Algebra and Matrices](https://web.archive.org/web/20140824074655/http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf) - Martin Fluch
* 📝 [Vector Space Theory](http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf) - Robert Howlett
* 📝 [Linear Algebra](http://joshua.smcvt.edu/linearalgebra) - Jim Hefferon
* 📝 [MIT OpenCourseWare Lectures on Linear Algebra (18.06) as [Jupyter](/@harrisonqian/awesome/wiki/miscellaneous/jupyter) Notebooks](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper
* 📝 [Elementary Linear Algebra](http://www.numbertheory.org/book/) - Keith Matthews
* 📝 [A First Courses in Linear Algebra](http://linear.ups.edu/) - Rob Breezer
* 📝 [Linear Algebra](https://www.math.ucdavis.edu/~linear/) - David Cherney, Tom Denton, Andrew Waldron
* 📝 [Introduction to vectors and tensors, Vol 1: linear and multilinear algebra](http://oaktrust.library.tamu.edu/handle/1969.1/2502) - Ray M Bowen, C. C. Wang
* 📝 [Introduction to vectors and tensors, Vol 2: vector and tensor analysis](http://oaktrust.library.tamu.edu/handle/1969.1/3609) - Ray M Bowen, C. C. Wang
* 📝 [Introduction to Applied Linear Algebra](https://web.stanford.edu/~boyd/vmls/vmls.pdf) - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
* 📝 [Linear Algebra Done Wrong](https://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf) - Sergei Treil
* 📝 [Immersive Linear Algebra](http://immersivemath.com/ila/index.html) - J. Ström, K. Åström, and T. Akenine-Möller
* 📝 [Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/) - Dan Margalit and Joseph Rabinoff
* 📝 [Linear Algebra, Infinite Dimensions, and Maple](https://people.math.gatech.edu/~herod/Hspace/Hspace.html) - James Herod
* 📖 [Linear Algebra Done Right](https://linear.axler.net/) - Sheldon Axler

### Ring Theory

* 📝 [Foundations of Module and Ring Theory](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf) - Robert Wisbauer (University of Düsseldorf)

### Galois Theory

* 📝 [An Introduction to Galois Theory](http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf) - Andrew Baker (University of Glasgow)
* 📝 [Fields and Galois Theory](http://www.jmilne.org/math/CourseNotes/FT.pdf) - J.S. Milne
* 📝 [Galois theory](http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf) - Miles Reid
* 📝 [Galois Theory](https://eclass.uoa.gr/modules/document/file.php/MATH594/Stewart%20Galois%204th%20edition.pdf) - Ian Stewart
* 📝 [Galois Theory](https://arxiv.org/pdf/2408.07499) — Tom Leinster (University of Edinburgh)

### Lie Algebras

* 📝 [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg

## Combinatorics

* 📝 [Basic Combinatorics](http://web.math.utk.edu/~wagner/papers/comb.pdf) - Carl G. Wagner (University of Tennessee)
* 📝 [Applied Combinatorics](http://people.math.gatech.edu/~trotter/book.pdf) - Mitchel T. Keller, William T. Trotter
* 📝 [Notes on Combinatorics](http://www.maths.qmul.ac.uk/~pjc/notes/comb.pdf) - Peter J. Cameron
* 📝 [Analytic Combinatorics](http://algo.inria.fr/flajolet/Publications/book.pdf) - Philippe Flajolet, Robert Sedgewick
* 📝 [generatingfunctionology](http://www.math.upenn.edu/~wilf/DownldGF.html) - Herbert Wilf

### Graph Theory

* 📝 [Graph Theory: Lecture Notes](http://www.personal.psu.edu/cxg286/Math485.pdf) - Christopher Griffin
* 📝 [Graph Theory](http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf) - Reinhard Diestel
* 📝 [Graph Theory : Interactive Algorithm Visualizer | Graph Theory [Learning](/@harrisonqian/awesome/wiki/programming-languages/learning) Platform](https://learngraphtheory.org/) - Hadjoudj Mohammed Islam 

## Geometry and Topology

* 📝 [Fundamentals of Geometry](http://polly.phys.msu.ru/~belyaev/geometry.pdf) - Oleg A. Belyaev
* 📝 [A=B](https://www.math.upenn.edu/~wilf/AeqB.html) - M. Petkovsek, H. Wilf, D. Zeilberger
* 📝 [Elements](http://aleph0.clarku.edu/~djoyce/java/elements/toc.html) - Euclid
* 📝 [Euclid's Elements Redux](http://starrhorse.com/euclid/) - Daniel Callahan
* 📝 [Mathematical Illustrations](http://www.math.ubc.ca/~cass/graphics/manual/) - Bill Casselman
* 📝 [Byrne's Euclid](https://www.c82.net/euclid/) - Oliver Byrne
* 📝 [Plane Geometry](http://djm.cc/library/Plane_Geometry_Wentworth_Smith_edited.pdf) - George Wentworth and David Eugene Smith (1913)
* 📝 [Planes and Spherical Trigonometry](http://djm.cc/library/Plane_Spherical_Trigonometry_Wentworth_Smith_edited_2.pdf) - George Wentworth and David Eugene Smith (1915)
* 📝 [Coordinate Geometry](http://djm.cc/library/Coordinate_Geometry_Fine_Thompson_edited03.pdf) - Henry Buchard Fine and Henry Dallas Thompson (1911)
* 📝 [Analytic Geometry](http://djm.cc/library/Analytic_Geometry_Siceloff_Wentworth_Smith_edited.pdf) - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922)

### Differential Geometry

* 📝 [Introduction to Differential Geometry](https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf) - Joel W. Robbin, Dietmar A. Salamon
* 📝 [Notes on Differential Geometry and Lie Groups](https://www.cis.upenn.edu/~jean/gbooks/manif.html) - Jean Gallier (University of Pennsylvania)
* 📝 [Topics in Differential Geometry](http://www.mat.univie.ac.at/~michor/dgbook.pdf) - Peter W. Michor
* 📝 [Lectures on Differential Geometry](http://mysite.science.uottawa.ca/rossmann/Differential%20Geometry%20book_files/Diffgeo.pdf) - Wulf Rossmann
* 📝 [An Introduction to Riemannian Geometry](http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf) - Sigmundur Gudmundsson (Lund University)
* 📝 [The Geometry and Topology of Three-Manifolds](http://msri.org/publications/books/gt3m/) - W. Thurston
* 📝 [Semi-Riemann Geometry and General Relativity](http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf) - Shlomo Sternberg
* 📝 [Discrete Differential Geometry](http://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf) - Keenan Crane

### Algebraic Geometry

* 📝 [A Brief Introduction to Algebraic Geometry](https://ksda.ccny.cuny.edu/PostedPapers/rickksda1107.pdf) - R.C. Churchill
* 📝 [Introduction to Algebraic Geometry](http://www.math.lsa.umich.edu/~idolga/631.pdf) - Igor V. Dolgachev
* 📝 [Foundations of Algebraic Geometry](http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf) - Ravi Vakil
* 📝 [Algebraic Geometry](http://www.cis.upenn.edu/~jean/algeoms.pdf) - Jean Gallier, Stephen S. Shatz (University of Pennsylvania)
* 📝 [Algebraic Geometry](http://www.jmilne.org/math/CourseNotes/AG.pdf) - J.S. Milne
* 📝 [Algebraic Geometry](http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf) - Andreas Gathmann (University of Kaiserslautern)
* 📝 [The [Stacks](/@harrisonqian/awesome/wiki/miscellaneous/stacks) Project](https://stacks.math.columbia.edu/) - Maintained by Aise Johan de Jong (Columbia)

### Algebraic Statistics
* 📝 [Lectures on Algebraic Statistics](https://math.berkeley.edu/~bernd/owl.pdf) - Mathias Drton, Bernd Sturmfels, Seth Sullivant
* 📝 [An Introduction to Algebraic Statistics](https://www3.diism.unisi.it/~chiantini/did/00Book.pdf) - Cristiano Bocci, Luca Chiantini and Anthony V. Geramita
* 📝 [Algebraic Statistics](https://tore.tuhh.de/dspace-cris-server/api/core/bitstreams/a0c378d5-ce8e-442a-8891-9e7f763b4279/content) - Karl-Heinz Zimmermann
* 📝 [Algebraic Statistics for Computational Biology](http://yaroslavvb.com/papers/pachter-algebraic.pdf) - Pachter, and Sturmfels.

### Topology

* 📝 [General Topology](https://www.rexresearch1.com/TopologyLibrary/GeneralTopologyWillard.pdf) - Stephen Willard
* 📝 [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) - Robert Ghrist (UPenn)
* 📝 [Introduction to Topology](http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf)
* 📝 [Introduction to Topology](http://www.math.bme.hu/~kalex/Teaching/Spring10/Topology/TopNotes_Spring10.pdf) - Alex Küronya
* 📝 [Introductory Topology](http://www.math.clemson.edu/~jimlb/Teaching/2009-10/Math986/Topology.pdf) - Jim L. Brown
* 📝 [General Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/Topo.pdf) - Pierre Schapira (Paris VI University)
* 📝 [Elementary Topology Problem Textbook](http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf)
* 📝 [General Topology](http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf) - Jesper M. Møller
* 📝 [Topology Topics](http://mathonline.wikidot.com/topology)

### Algebraic Topology

* 📝 [Algebraic Topology](http://pi.math.cornell.edu/~hatcher/AT/AT.pdf) - Allen Hatcher
* 📝 [A Concise Course in Algebraic Topology](http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf) - J. P. May
* 📝 [Introduction to Algebraic Topology](http://www.math.muni.cz/~cadek/at/at.pdf) - Martin Cadek
* 📝 [Algebra and Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/AlTo.pdf) - Pierre Schapira (Paris VI University)
* 📝 [Lecture Notes in Algebraic Topology](http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf) - James F. Davis, Paul Kirk (Indiana University)
* 📝 [Algebraic Topology](https://www.ma.utexas.edu/ibl1/courses/resources/12_15_07_grad_alg_top_mooremethod.pdf) - Michael Starbird
* 📝 [Lecture Notes on Algebraic Topology](http://www.math.nus.edu.sg/~matwujie/ma5209.pdf) - Jie Wu

## Analysis

### Real Analysis

* 📝 [MIT OpenCourseWare Lectures on Calculus](https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/) - G. Strang
* 📝 [Elementary Calculus: An Approach Using Infinitesimals](http://www.math.wisc.edu/~keisler/calc.html) - Professor H. Jerome Keisler
* 📝 [An Introduction to Real Analysis](https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf) - John K. Hunter (University of California at Davis)
* 📝 [Introduction to Real Analysis](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF) - William F. Trench (Trinity University, Texas)
* 📝 [Basic Analysis: Introduction to Real Analysis](http://www.jirka.org/ra/realanal.pdf) - Jiří Lebl
* 📝 [Elementary Real Analysis](http://prac.im.pwr.wroc.pl/~kwasnicki/pl/stuff/tbb-[hyper](/@harrisonqian/awesome/wiki/development-environment/hyper).pdf) - Thomson, Bruckner
* 📝 [Lecture Notes in Real Analysis](http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf) - Eric T. Sawyer (McMaster University)
* 📝 [Real Analysis](http://math.harvard.edu/~ctm/papers/home/text/class/harvard/212a/course/course.pdf) - C. McMullen
* 📝 [Real Analysis for Graduate Students](http://bass.math.uconn.edu/3rd.pdf) - Richard F. Bass
* 📝 [Modern Real Analysis](http://www.math.purdue.edu/~torres/pubs/Modern-real-analysis.pdf) - William P. Ziemer (Indiana University)
* 📝 [Mathematical Analysis Vol I](http://www.trillia.com/zakon-analysisI.html) - Elias Zakon
* 📝 [Mathematical Analysis Vol II](http://www.trillia.com/zakon-analysisII.html) - Elias Zakon
* 📝 [Advanced Calculus](http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf) - Lynn Loomis, Schlomo Sternberg
* 📝 [ Analysis of Functions of a Single Variable](http://spot.colorado.edu/~baggett/analysis.html) - Lawerence Baggett
* 📝 [The Calculus of Functions of Several Variables](http://www.synechism.org/wp/the-calculus-of-functions-of-several-variables/) - Dan Sloughter
* 📝 [A ProblemText in Advanced Calculus](http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf) - John M. Erdman
* 📝 [Calculus and Linear Algebra. Vol. 1](http://hdl.handle.net/2027/spo.5597602.0001.001) - Wilfred Kaplan, Donald J. Lewis
* 📝 [Calculus and Linear Algebra. Vol. 2](https://quod.lib.umich.edu/s/spobooks/5597602.0002.001) - Wilfred Kaplan, Donald J. Lewis
* 📝 [Introduction to Calculus I and II](http://www.math.odu.edu/~jhh/counter10.html) - J.H. Heinbockel
* 📝 [Active Calculus](http://faculty.gvsu.edu/boelkinm/Home/Active_Calculus.html) - Matt Boelkins
* 📝 [Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis"](https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin) - George M. Bergman
* 📝 [Calculus Made Easy](http://calculusmadeeasy.org/) - Silvanus P. Thompson (1910)
* 📝 [Elements of Differential and Integral Calculus](http://djm.cc/library/Elements_Differential_Integral_Calculus_Granville_edited_2.pdf) - William Anthony Granville (1911)
* 📝 [Precalculus](https://stitz-zeager.com/szprecalculus07042013.pdf) - Carl Stitz, Jeff Zeager

### Harmonic Analysis

* 📝 [Harmonic Analysis Lecture Notes](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf) - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
* 📝 [Harmonic Analysis](http://www.math.uchicago.edu/~schlag/harmonicnotes.pdf) - W. Schlag
* 📝 [Lecture Notes: Fourier Transform and its Applications](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf) - Brad Osgood
* 📝 [Fourier Analysis](http://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf) - Lucas Illing
* 📝 [Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications](https://ccrma.stanford.edu/~jos/mdft) - Julius O. Smith III (Stanford University)

### Complex Analysis

* 📝 [Introduction to Complex Analysis](https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/complex.pdf) - Michael Taylor
* 📝 [An Introduction to Complex Analysis and Geometry](http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book-5-refs-bip.pdf) - John P. D'Angelo (University of Illinois)
* 📝 [A First Course in Complex Analysis](http://math.sfsu.edu/beck/papers/complex.pdf) - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
* 📝 [A Guide to Complex Variables](http://www.math.wustl.edu/~sk/books/guide.pdf) - Steven G. Krantz
* 📝 [Complex Analysis](http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex_analysis.pdf) - Charles Walkden
* 📝 [Complex Analysis](http://www.math.ku.dk/noter/filer/koman-12.pdf) - Christian Berg
* 📝 [Complex Variables](http://people.math.sc.edu/girardi/m7034/book/AshComplexVariablesWithHyperlinks.pdf) - R. B. Ash, W.P. Novinger
* 📝 [Complex Analysis](http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf) - Christer Bennewitz
* 📝 [Complex Analysis](https://web.archive.org/web/20150620124453/https://www.math.washington.edu/~marshall/math_536/Notes.pdf) - Donald E. Marshall
* 📝 [A Concise Course in Complex Analysis and Riemann Surfaces](https://gauss.math.yale.edu/~ws442/complex.pdf) - Wilhelm Schlag
* 📝 [Complex Analysis](http://people.math.gatech.edu/%7Ecain/winter99/complex.html) - G. Cain (Georgia Tech)
* 📝 [Complex Analysis](https://complex-analysis.com/) - Juan Carlos Ponce Campuzano

### Functional Analysis

* 📝 [An Introduction to Functional Analysis](https://www.math.uwaterloo.ca/~lwmarcou/notes/pmath453.pdf) - Laurent W. Marcoux (University of Waterloo)
* 📝 [Functional Analysis: Lecture Notes](http://users.math.msu.edu/users/jeffrey/920/920notes.pdf) - Jeff Schenker (Michigan State University)
* 📝 [Functional Analysis Lecture Notes](https://archive.org/details/TB_Ward___Functional_analysis_lecture_notes) - T.B. Ward (University of East Anglia)
* 📝 [Functional Analysis](http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf) - Alexander C. R. Belton
* 📝 [Topics in Real and Functional Analysis](https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf) - Gerald Teschl
* 📝 [Functional Analysis](http://www2.math.ou.edu/~cremling/teaching/lecturenotes/fa-new/LN-I.pdf) - Christian Remling

---
*truncated — [full list on GitHub](https://github.com/rossant/awesome-math)*
