In preparing this new edition I have tried to keep the changes to a minimum, on the principle that one should not meddle with a relatively successful text. Thus the general form of the book remains the same. Naturally I have taken the opportunity to correct the errors of which I was aware. Also the text has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included.

Preface to the Second Edition
Preface to the First Edition
Notation
CHAPTER 1 Fundamental Concepts of Group Theory
1.1. Binary Operations， Semigroups， and Groups
1.2. Examples of Groups
1.3. Subgroups and Cosets
1.4. Homomorphisms and Quotient Groups
1.5. Endomorphisms and Automorphisms
1.6. Permutation Groups and Group Actions
CHAPTER 2 Free Groups and Presentations
2.1. Free Groups
2.2. Presentations of Groups
2.3. Varieties of Groups
CHAPTER 3 Decompositions of a Group
3.1. Series and Composition Series
3.2. Some Simple Groups
3.3. Direct Decompositions
CHAPTER 4 Abielian Groups
CHAPTER 5 Soluble and Nilpotent Groups
CHAPTER 6 Free Groups and Free Products
CHAPTER 7 Finite Permuation Groups
CHAPTER 8 Representations of Groups
CHAPTER 9 Finite Soluble Groups
CHAPTER 10 The Transfer and Its Applications
CHAPTER 11 The Theory of Group Eltensions
CHAPTER 12 Generalization of Nilpotent and Soluble Groups
CHAPTER 13 Subnormal Subgroups
CHAPTER 14 Finiteness Properties
CHAPTER 15 Infinite Souluble Groups
Bibliography
Index