- nLab for abstract nonsense (and mLab for actual nonsense).
- Overleaf for collaborative LaTeX projects.
- Math Stackexchange and MathOverflow for questions.
- TeX Stackexchange for TeX support and Detexify for looking up symbols.
- Ti
*k*Z-cd for diagrams, and Yichuan Shen's editor or quiver for help getting started. - SageMath, GAP, Singular and Macaulay2 for computations.

- The Youtube channel 3blue1brown.
- The blog Math3ma.
- The podcast My Favorite Theorem.
- The blog Math ∩ Programming.
- The magazine Quanta Magazine.

- Living Proof.
- The forall Instagram account.
- Ravi Vakil's advise on seminars.
- Dan Margalit's resource pages.

- Category Theory in Context by Emily Riehl.
- The Catsters on Youtube.

- “Contemporary Linear Algebra” by Howard Anton and Robert C. Busby.
- Essense of Linear Algebra by 3blue1brown.
- “Finite-Dimensional Vector Spaces” by Paul R. Halmos.
- “Numerical Linear Algebra” by Lloyd N. Trefethen and David Bau, III.

- “Abstract Algebra: Theory and Applications” by Thomas W. Judson.

*A Sage-based introduction to abstract algebra. A lot of interesting exercises.* - “Algebra: Chapter 0” by Paolo Aluffi.
*Category-flavored introduction to algebra with a bit of humor.*

- “Ideals, Varieties, and Algorithms” and “Using Algebraic Geometry” by David A. Cox, John Little, and Donal O'shea.
- Introduction to Non-Linear Algebra by Mateusz Michalek and Bernd Sturmfels.
- Lecture notes on Commutative Algebra and Algebraic Geometry by Andreas Gathmann.
- The Rising Sea by Ravi Vakil.
- The Stacks Project.

- “Introduction to Tropical Geometry” by Diane Maclagan and Bernd Sturmfels.
- Twelve Lectures on Tropical Geometry by Bernd Sturmfels.
- An introduction to tropical geometry: theory and applications by Fatemeh Mohammadi.
- Lectures from the Algebraic and Tropical Online Meetings (ATOM).
- Tropical Geometry of Curves by Madeline Brandt.
- Essentials of Tropical Combinatorics by Michael Joswig.

- Applications of Polynomial Systems (a lecture series by David Cox and invited speakers).
- The NASO seminar in Leipzig.
- The Mathematics of Reaction Networks seminar.
- Biochemical reaction networks: An invitation to algebraic geometers by Alicia Dickenstein.
- The case for algebraic biology: From research to education by Matthew Macauley and Nora Youngs.
- Nonlinear algebra and applications by Paul Breiding et al.

- “Naive Lie Theory” by Stillwell.
*Very accessible, with many interesting historical remarks.* - “Lie Groups, Lie Algebras, and Representations” by Brian C. Hall.
- “Representations of Compact Lie Groups” by Theodor Bröcker and Tammo tom Dieck.
- “Lie Groups Beyond an Introduction” by Anthony Knapp.

- “Representation Theory” by William Fulton and Joe Harris.
- Lecture notes by Thomas Krämer.
- “Introduction to Representation Theory” by Pavel Etingof et al.
- “Quantum Groups” by Christian Kassel.

- “The Knot Book” by Colin C. Adams.
*Accessible for high school students!* - “Knot Theory” by Charles Livingston.
- “Knots Knotes” by Justin Roberts.
- “An Introduction to Knot Theory” by Raymond Lickorish.
- The Knot Atlas.
- Videos from Roger Fenn's and Louis Kauffman's 2020 knot theory course.
- Virtual Low-Dimensional Topology.

- “An Introduction to Homological Algebra” by Joseph J. Rotman.
- An 80 minutes introduction to homological algebra by Rishi Vyas.
- The snake lemma makes a short (and perfectly accurate!) cameo in It's My Turn (1980).
- “A User's Guide to Spectral Sequences” by John McCleary.

- “Topology” by James Munkres.
- “Introduction to Topological Manifolds” by John M. Lee.
- “Topology from a Differentiable Viewpoint” by John W. Milnor.
- “Algebraic Topology” by Allen Hatcher.
- Lectures on Introductory Algebraic Topology by Pierre Albin.
- Lecture notes by James F. Davis and Paul Kirk.
- “A Concise Course in Algebraic Topology” by Peter May.

- “Differential Geometry of Curves and Surfaces” by Kristopher Tapp.
- “Introduction to Smooth Manifolds” by John M. Lee.
- “Riemannian Geometry” by Sigmundur Gudmundsson.
- Lectures on Geometrical Anatomy of Theoretical Physics by Fredric Schuller.
- “Riemannian Manifolds: An Introduction to Curvature” by John M. Lee.
- “Riemannian Geometry” by Manfredo do Carmo.
- “A Comprehensive Introduction to Differential Geometry” by Michael Spivak.

- “Introductory Functional Analysis with Applications” by Erwin Kryszig.
- “A Course in Functional Analysis” by John B. Conway.
- Lecture notes by Alan Sokal.

- A Mathematician’s Lament by Paul Lockhart.
- The Ideal Mathematician by Phillip J. David and Reuben Hersh.

- Practical suggestions for mathematical writing by Bjorn Poonen
- A TeX Stackexchange thread about things to check in software-generated bibliographic entries.
- Mathematical Writing by by Donald Knuth, Tracy Larrabee, and Paul Roberts.

- “Mathematics++” by Ida Kantor, Jiří Matousek and Robert Šámal.

*Computer-scientifically flavored introductions to measure theory, Fourier analysis, representation theory, algebraic geometry and topology.* - Keith Conrad’s notes collection on a wide array of subjects.
- An Infinitely Large Napkin by Evan Chen.
- “Introduction to Experimental Mathematics” by Søren Eilers and Rune Johansen.

- Finite Simple Group (of Order Two) by The Klein Four (and everything else on the album Musical Fruit Cake).
- The Grothendieck Song by Richard Elwes.
- “Mathematics Made Difficult” by Carl E. Linderholm.
- Acme Klein Bottles.

- Zack Garza’s list of resources.
- Tai-Danae Bradley's list of resources for intro-level grad courses.
- Chicago undergraduate mathematics bibliography.