I'm looking for a good (intoductionary) book on group theory that treats (at least) the following material:
The axioms of groups, commutativity, symmetrical groups, permutation groups; Cayley's theorem, matrix groups, order of a group, homomorphisms between groups, isomorphisms between groups, undergroups; Lagrange's theorem, quotient groups; normal undergroups, homomorphesm, kernal, image, isomorphism theorems, group actions; the orbit stabilisator theorem, direct products of groups, the cauchy theorem, sylowgroups; Sylow's theorem and "free" group.
The book the course recommends is: Armstrong, M.'s Groups and symmetry.
That said, I've found that I usually get much better book recommendations by asking around on here. When it comes to personal preference, I enjoyed Kunze's Linear algebra and Rudin's Mathematical Analysis. I prefer books not be too verbose in their approach to the subject and am okay with losing (some of) a proof's detail in favour of a clear portrayal of the important steps (I believe Rudin does this really well).