Now in paperback, this advanced text on Cohen-Macaulay rings has been updated and expanded.This text emphasizes the study of explicit, specific rings, making the presentation as concrete as possible. The general theory is applied to a number of examples and the connections with combinatorics are highlighted. Throughout each chapter are many examples and exercises.This text emphasizes the study of explicit, specific rings, making the presentation as concrete as possible. The general theory is applied to a number of examples and the connections with combinatorics are highlighted. Throughout each chapter are many examples and exercises.In the past two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the subject. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. The general theory is applied to a number of examples and the connections with combinatorics are highlighted. Throughout each chapter, the authors have supplied many examples and exercises.1. Regular sequences and depth; 2. Cohen-Macaulay rings; 3. The canonical module. Gorenstein rings; 4. Hilbert functions and multiplicities; 5. Stanley-Reisner rings; 6. Semigroup rings and invariant theory; 7. Determinantal rings; 8. Big Cohen-Macaulay modules; 9. Homological theorems; 10. Tight closure.}}} }}} a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen}}}Macaulay rings }}} very useful for graduate courses in algebra. As the only modern, broad account of the subject, it will be essential reading for specialists as well.}}} L}}}Enseignement Math}}matique}}}This book presents basic results in commutative algebra together with their applications in different special fields. It can be read immediately after an introductory text, but it brings you quickly to the main problems of the topic }}} A@M