Algebra (3^rd Ed., 3rd rev. ed. 2002. Corr. 4th printing 2005)
Graduate Texts in Mathematics Series, Vol. 211

This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."

Foreword * Groups * Rings * Modules * Polynomials * Algebraic Equations * Galois Theory * Extensions of Rings * Transcendental Extensions * Algebraic Spaces * Noetherian Rings and Modules * Real Fields * Absolute Values * Matrices and Linear Maps * Representation of One Endomorphism * Structure of Bilinear Forms * The Tensor Product * Semisimplicity * Representations of Finite Groups * The Alternating Product * General Homology Theory * Finite Free Resolutions * Appendices * Bibliography