This book is a comprehensive text on modules and rings, written by T. Y. Lam. It is part of the Graduate Texts in Mathematics series published by Springer-Verlag. The book is structured into nineteen sections, which are numbered consecutively and are independent of the seven chapters. The text is intended for graduate students and researchers in mathematics, particularly those interested in ring theory and module theory. The book begins with an introduction to modules and rings, covering topics such as free modules, projective modules, injective modules, and flat modules. It then delves into homological dimensions, uniform dimensions, and the theory of rings of quotients. The text also includes a detailed discussion on Frobenius and quasi-Frobenius rings, as well as Morita theory and duality theory. The book is written in a clear and concise manner, with a focus on examples and exercises. It includes a large number of exercises, ranging from routine to challenging, which help reinforce the concepts presented. The text also provides a detailed list of notations and abbreviations, making it easier for readers to navigate the material. The book is divided into seven chapters, each covering a specific topic in ring theory and module theory. The first chapter introduces the basic concepts of modules and rings, while the second chapter discusses projective and injective modules. The third chapter covers flat modules and homological dimensions, and the fourth chapter discusses uniform dimensions, complements, and CS modules. The fifth chapter focuses on singular submodules and nonsingular rings, while the sixth chapter discusses dense submodules and rational hulls. The seventh chapter covers rings of quotients, including noncommutative localization and classical rings of quotients. The eighth chapter discusses maximal rings of quotients, and the ninth chapter covers Martindale rings of quotients. The tenth chapter discusses Frobenius and quasi-Frobenius rings, while the eleventh chapter covers matrix rings, categories of modules, and Morita theory. The twelfth chapter discusses Morita duality theory, and the thirteenth chapter covers the notes to the reader, which provide additional information and guidance for readers. The book concludes with a list of references and an index for quick reference.This book is a comprehensive text on modules and rings, written by T. Y. Lam. It is part of the Graduate Texts in Mathematics series published by Springer-Verlag. The book is structured into nineteen sections, which are numbered consecutively and are independent of the seven chapters. The text is intended for graduate students and researchers in mathematics, particularly those interested in ring theory and module theory. The book begins with an introduction to modules and rings, covering topics such as free modules, projective modules, injective modules, and flat modules. It then delves into homological dimensions, uniform dimensions, and the theory of rings of quotients. The text also includes a detailed discussion on Frobenius and quasi-Frobenius rings, as well as Morita theory and duality theory. The book is written in a clear and concise manner, with a focus on examples and exercises. It includes a large number of exercises, ranging from routine to challenging, which help reinforce the concepts presented. The text also provides a detailed list of notations and abbreviations, making it easier for readers to navigate the material. The book is divided into seven chapters, each covering a specific topic in ring theory and module theory. The first chapter introduces the basic concepts of modules and rings, while the second chapter discusses projective and injective modules. The third chapter covers flat modules and homological dimensions, and the fourth chapter discusses uniform dimensions, complements, and CS modules. The fifth chapter focuses on singular submodules and nonsingular rings, while the sixth chapter discusses dense submodules and rational hulls. The seventh chapter covers rings of quotients, including noncommutative localization and classical rings of quotients. The eighth chapter discusses maximal rings of quotients, and the ninth chapter covers Martindale rings of quotients. The tenth chapter discusses Frobenius and quasi-Frobenius rings, while the eleventh chapter covers matrix rings, categories of modules, and Morita theory. The twelfth chapter discusses Morita duality theory, and the thirteenth chapter covers the notes to the reader, which provide additional information and guidance for readers. The book concludes with a list of references and an index for quick reference.