本书以作者在莫斯科大学讲演稿为蓝本，主要目的是尽可能简明、详尽地将遇到的问题阐述清楚。书中全面展示有限群和紧群线性表示理论基础知识，给出了李群线性表示理论的基本知识以及李群表示论的一些基本观点，详尽讲述了群SU2和SO2表示论部分，作为应用仔细推导了拉普拉斯球面函数。书中有一些例子和练习，并对部分习题附有解答。

Preface

Introduction

 0 Basic Notions

I General Properties of Representations

 1 Invariant Subspaces

 2 Complete Reducibility of Representations of Compact Groups

 3 Basic Operations on Representations

 4 Properties of Irreducible Complex Representations

II Representations of Finite Groups

 5 Decomposition Of the Regular Representation

 6 Orthogonality Relations

III Representations of Compact Groups

 7 The Groups SU2 and SO3

 8 Matrix Elements of Compact Groups

 9 The Laplace Spherical Functions

IV Representations of Lie Groups

 10 General Properties of Homomorphisms and Representations of Lie Groups

 11 Representations of SU2 and SO3

Appendices

 A1 Presentation of Groups By Means of Generators and Relations

 A2 Tensor Products

 A3 The Convex Hull of a Compact Set

 A4 Conjugate Elements in Groups

Answers and Hints to Exercises

List of Notations

References

Index