I quite like Pinter’s “A Book of Abstract Algebra”. He writes very cleanly, is aimed at beginners, but doesn’t cut corners.

If you’re already pretty serious about math (i.e., you already write proofs; maybe you took an analysis class), then I recommend Artin’s Algebra.

If you really want tons of practice and a Stewart’s Calculus-like book, then Dummit and Foote.