●CHAPTER Ⅰ
Lie Groups and Lie Algebras
1.The Concept of a Lie Group and the Classical Examples
2.Left—Invariant Vector Fields and One—Parameter Groups
3.The Exponential Map
4.Homogeneous Spaces and Quotient Groups
5.Invariant Integration
6.Clifford Algebras and Spinor Groups
CHAPTER Ⅱ
Elementary Representation Theory
1.Representations
2.Semisimple Modules
3.Linear Algebra and Representations
4.Characters and Ortho Sonality Relations
5.Representations of SU（2）， SO（3）， U（2）， and O（3）.
6.Real and Quaternionic Representations
7.The Character Ring and the Representation Ring
8.Representation of Abelian Groups
9.Representations of Lie Algebras
10.The Lie Algebra sl（2，C）
CHAPTER Ⅲ
Representative Functions
1.Algebras of Representative Functions
2.Some Analysis on Compact Groups
3.The Theorem of Peter and Weyl
4.Applications of the Theorem of Peter and Weyl
5.Generalizations of the Theorem of Peter and Weyl
6.Induced Representations
7.Tannaka—Krein Duality
8.The Complexification of Compact Lie Groups
CHAPTER Ⅳ
The Maximal Torus of a Compact Lie Group
1.Maximal Tori
2.Consequences of the Conjugation Theorem
3.The Maximal Tori and Weyl Groups of the Classical Groups
4.Cartan Subgroups of Nonconnected Compact Oroups
CHAPTER Ⅴ
Root Systems
1.The Adjoint Representation and Groups of Rank I
2.Roots and Weyl Chambers
3.Root Systems
4.Bases and Weyl Chambers
5.Dynkin Diagrams
6.The Roots of the Classical Groups
7.The Fundamental Group， the Center and the Stiefel Diagram
8.The Structure of the Compact C，roups
CHAPTER Ⅵ
Irreducible Characters and Weights
1.The Weyl Character Formula
2.The Dominant Weight and the Structure of the Representation Ring
3.The ltiplicities of the Weights of an Irreducible Representation
4.Representations of Real or Quatemionic Type
5.Representations of the Classical Groups
6.Representations of the Spinor Groups
7.Representations of the Orthogonal Groups
Bibliography
Symbol Index
Subject Index

這本書是基於作者1966年以來的講義撰寫而成，主要介紹緊李群理論。該書主要由六部分組成，每部分又有不同的章節構成，每章最後還有讓讀者自測的小練習。目次：李群和李代數；理論的基本表示；代表性的函數；緊李群的優選圓環體；根的形式；不可約的字符和變量；字符索引。讀者對像：大學高年級本科生，低年級研究生。

(德)T.布羅克(Theodor Brocker) 著 著