Getting into group theory
Group theory is the mathematics of symmetry: moves you can combine and undo. Here are three ways in, and they all link into each other.
New to group theory? Start here for a quick readiness check, what to read alongside, and which guide to open first.
What everyone asks
A guide built from the 2,000 most upvoted group theory questions on Math Stack Exchange, in course order.
The biggest chapter is people proving that things commute.
Thirty problems
No explanations. Go from the axioms to the simplicity of $A_5$, with hints and a permutation scratchpad.
Problem 14 is why the 15-puzzle can't be solved.
A field guide to groups
Thirteen small groups drawn as coloured multiplication tables, and a key that identifies any group you build.
$D_4$ and $Q_8$ agree on almost everything.
Also in this series: linear algebra.