Introduction 1
0．Basic Notions 1
Ⅰ．General Properties of Representations 13
1．Invariant Subspaces 13
2．Complete Reducibility of Representations of Compact Groups 22
3．Basic Operations on Representations 30
4．Properties of Irreducible Complex Representations 44
Ⅱ．Representations of Finite Groups 55
5．Decomposition of the Regular Representation 55
6．Orthogonality Relations 66
Ⅲ．Representations of Compact Groups 73
7．The Groups SU2 and SO3 73
8．Matrix Elements of Compact Groups 80
9．The Laplace Spherical Functions 85
Ⅳ．Representations of Lie Groups 93
10．General Properties of Homomorphisms and Representations of Lie Groups 93
11．Representations of SU2 and SO3 109
Appendices 117
A1 Presentation of Groups By Means of Generators and Relations 117
A2 Tensor Products 124
A3 The Convex Hull of a Compact Set 129
A4 Conjugate Elements in Groups 131
Answers and Hints to Exercises 133
List of Notations 139
References 141
Index 143