Abstract Algebra

Below is a list of reviews of books on abstract algebra.

Basic Algebra I
Jacobson, N. (2nd Ed. 1985). Free Download
Prerequisites: comfort with proof-based mathematics, basic linear algebra for some chapters.

Very solid treatment of standard material in a two-semester abstract algebra sequence in the first four chapters, with good exposition and exercises. Contains and additional four chapters which go over less-standard material like lattices.

Algebra
Lang, S. (3rd Ed. 2002). ISBN 9780387953854.
Proof writing. Background in analysis will help with understanding some examples.

Starts with the basics and rapidly builds up to cover a wide variety of topics, from group solvability to Galois Theory. This book is difficult to read without prior experience in algebra, and leaves a significant portion of the proofs as “exercise to the reader,” despite many of them being highly nontrivial. However, used as a second textbook in algebra, its strength in the terseness of the proofs becomes apparent. A determined reader can cover significant amounts of material in a relatively short period of time using this book. The exercises in the book can be quite difficult, but they provide solid understanding of how to apply the theory from the preceding chapter.

Abstract Algebra
Dummit, S., Foote., M. (3rd Ed. 2003). Free Download

The classic for a course on this subject and for a good reason. First of all, the book is extremely comprehensive for a first course on algebra, and it is split into parts covering group theory, ring theory, module theory, field theory, algebraic geometry, commutative algebra, homological algebra, and representation theory. It contains far more than a single course in algebra can cover, but the explanations are always clear. The thing I loved most about this text was the wealth of different examples and exercises which had a very good range in difficulty from simple checks in understanding to problems that made me think about the topics for a long and sustained time. The only caution I will give is that the book is often said to be dry.