A pretty good book for abstract algebra is Pinter's "A Book of Abstract Algebra". It's rigorous but not overly terse and provides enough examples and applications as it goes to motivate the student. Chapters are fairly short and end with a large number of exercises, organized by topic, to give you plenty of opportunity to practice the material.

It's available in a Dover edition for under $16 so it is easy on the budget too [1].

[1] https://www.amazon.com/Book-Abstract-Algebra-Second-Mathemat...