The book is part of the world-renowned encyclopedia of modern mathematics, created by a group of French scientists acting under the collective pseudonym N. Bourbaki. All books in this series are distinguished by originality and high scientific level. A significant part of them is translated or translated into Russian. This book consists of seven chapters and contains an exposition of a number of the most important issues of homological algebra, the theory of primitive decomposition, the theory of whole elements and normalizations, and many other sections of commutative algebra - one of the fundamental areas of modern mathematics.