This book, contains more than enough material for a two-semester graduate-level abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. This book could be used for self study as well as for a course text, and so full details of almost all proofs are included. There are hundreds of problems, many being far from trivial.

1. Definitions and Examples of Groups
2. Subgroups and Cosets
3. Homomorphisms
4. Group Actions
5. The Sylow Theorems and p-groups
6. Permutation Groups
7. New Groups from Old
8. Solvable and Nilpotent Groups
9. Transfer
10. Operator Groups and Unique Decompositions
11. Module Theory without Rings
12. Rings, Ideals, and Modules
13. Simple Modules and Primitive Rings
14. Artinian Rings and Projective Modules
15. An Introduction to Character Theory

1. Polynomial Rings, PIDs, and UFDs
2. Field Extensions
3. Galosis Theory
4. Separability and Inseparability
5. Cyclotomy and Geometric Constructions
6. Finite Fields
7. Roots, Radicals, and Real Numbers
8. Norms, Traces, and Discriminants
9. Transcendental Extensions
10. The Artin-Schreier Theorem
11. Ideal Theory
12. Noetherian Rings
13. Integrality
14. Dedekind Domains
15. Algebraic Sets and the Nullstellensatz