This book is translated from the Chinese version published by Science Press, Beijing, China, in 2017. It was written for the Chern class in mathematics of Nankai University and has been used as the textbook for the course Abstract Algebra for this class for more than five years. It has also been adapted in abstract algebra courses in several other distinguished universities across China.The aim of this book is to introduce the fundamental theories of groups, rings, modules, and fields, and help readers set up a solid foundation for algebra theory. The topics of this book are carefully selected and clearly presented. This is an excellent mathematical exposition, well-suited as an advanced undergraduate textbook or for independent study. The book includes many new and concise proofs of classical theorems, along with plenty of basic as well as challenging exercises.Key Features: oMany proofs of classical theorems are new or concise, e.g., Sylow’s Theorems, L K Hua’s Theorem on semi-homomorphisms of ringsoThe introduction of new concepts and ideas is natural and motivative, e.g., the definition of free modules, the introduction of Galois extension, etc.oExercises are many and related to various fields of mathematics, e.g., there are many exercises related to number theory, differential geometry, etc.

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