本书讲述李群的基本理论及其应用，共六章。第一章介绍紧致群的线性表示论；第二章详细说明如何去实现李群结构的线性化和李代数在李群结构论上的基本重要性；第三章研讨连通紧致李群的伴随变换群的轨几何；第四章得出紧致李群的结构和分类理论；第五章用代数的观点，讨论复半单李代数的结构与分类；第六章则涉及实半单李代数的理论，特别是它与对称空间理论的联系。

This book discusses Li group's basic theory and its applications, consisting of six chapters. Chapter 1 introduces the linear representation theory of compact groups; Chapter 2 provides a detailed explanation of how to linearize Lie group structures and the fundamental importance of Lie algebra in Lie group structure theory; Chapter 3 discusses the orbital geometry of the adjoint transformation group of connected compact Lie groups; Chapter 4 presents the structure and classification theory of compact Lie groups; Chapter 5 discusses the structure and classification of complex semi simple Lie algebras from an algebraic perspective; Chapter 6 deals with the theory of real semi simple Lie algebras, particularly its connection with the theory of symmetric spaces.