Commutative Algebra

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

Introduction to Commutative Algebra
Atiyah, M., Macdonald, F. C. (1994) ISBN 9780201407518.
Prerequisites: basic group and ring theory, point-set topology

Very terse and dense introduction to commutative algebra including treatment of module theory, localization, integral extensions, Noetherian and Artinian rings, and more. Heavy on exercises and uses them to develop a lot of the theory, particularly connections to geometry. Recommended for people willing to do most of the exercises in each chapter and who enjoy dense presentation with minimal exposition or fluff.

Commutative Algebra
Gathmann, A. (2013). Free Download
Class notes as taught at the TU Kaiserslautern. Prerequisites are a standard introduction to algebra.

Very down to earth and accessible introduction to commutative algebra that emphasizes its connection to algebraic geometry and algebraic geometry as a source of intuition for the algebraic statements. As those are class notes, they don’t cover as much as other books on the subject, but the most important constructions are present. Exercises are included in the text and appear close to the introduction of the tools, which are required to solve them.