Mathematics

Remarks

If a link does not work, search the textbook on LibGen... they probably have it.

Multiple books on the same topic is better than a single "best" book on the topic.

Self-learning comes with self-research outside of textbooks or lectures.

Calculus and linear algebra are pretty much required to understand the rest of math. Everything after that is a matter of personal choice.

Useful references

Channels

MIT, Borcherds, Numberphile, Mathemaniac, Faculty, Schuller

Funny/fun things

Marianopolis

Introduction to Mathematics

"Calculus, Linear Algebra"

Analysis

"Continuity"

Abstract algebra

"Isomorphism"

Topology

"Invariants"

Number theory

"Primes"

Mathematical Logic

"Proofs"

Misc

Contest math

Contests

Waterloo contests, COMC contest, AMC contest, MIT integration bee, Miklos Schweitzer contest, Putnam contest, APMO contest, IMO contest

Resources

Articles and scholarly

Not exhaustive: SciHub (our holy savior), Arxiv.org, MathSciNet, Zentralblatt, Worldcat, Google scholar, MIT newd, Phys.org, Nature, Science, PNAS, Quanta magazine, MIT libguides, Oxford libguides, Stanford libguides, Princeton libguides, Cambridge libguides, Harvard libguides