TITLE: Requesting abstract algebra book recommendations
QUESTION [41 upvotes]: I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.
I was thinking of trying abstract algebra. I would appreciate any book recommendations.
Thanks in advance.
Andrew

REPLY [3 votes]: It depends on which subject your interested in particular.  Here is a list of the books if find go in the greatest depth and yield the clearest intuition on each major subject:

Familiar Structures:

Fields: Stacks Project Chapter 9
Modules (Vector Spaces):Rotman, Homological Algebra: Chapter 1, Bourbaki, Vol 1-3
Algebras: Matsumura, Bourbaki, Vol 1-3, Milne AGS, Chapter 2 (also discusses Co-algebras)
Rings: Lectures Anderson, Bourbaki, Vol 1-3, Rotman, Homological Algebra: Later Chapters


Abstract Structures:

Homological Algebra: Weibel, Enochs, Stacks Project Chapter 12
Groups: Serre's LROFG, Dummit and Foote/ Groupoids: Stacks Project: Chapter 38, section 13/ Algebraic Groups/ Lie Groups (good introduction)
Categories: MacLane Categories (a classic and my favorite), Kelly's Enriched Categories, Stacks Project