CONTENTS
Preface = Ⅶ
Acknowledgements = Ⅶ
ChapterⅠ History
1. Introduction = 1
2. The beginnings = 1
3. Finitely presented groups = 2
4. More history = 5
5. Higman's marvellous theorem = 8
6. Varieties of groups = 9
7. Small Cancellation Theory = 14
Chapter Ⅱ The Weak Burnside Problem
1. Introduction = 17
2. The Grigorchuk-Gupta-Sidki groups = 19
3. An application to associative algebras = 27
Chapter Ⅲ Free groups, the calculus of presentations and the method of Reidemeister and Schreier
1. Frobenius' representation = 29
2. Semidirect products = 33
3. Subgroups of free groups are free = 37
4. The calculus of presentations = 47
5. The calculus of presentations(continued) = 49
6. The Reidemeister-Schreier method = 55
7. Generalized free products = 58
Chapter Ⅳ Recursively presented groups, word problems and some applications of the Reidemeister-Schreier method
1. Recursively presented groups = 61
2. Some word problems = 63
3. Groups with free subgroups = 64
Chapter Ⅴ Affine algebraic sets and the representative theory of finitely generated groups
1. Background = 75
2. Some basic algebraic geometry = 76
3. More basic algebraic geometry = 80
4. Useful notions from topology = 82
5. Morphisms = 85
6. Dimension = 90
7. Representations of the free group of rank two in SL(2, C) = 93
8. Affine algebraic sets of characters = 99
Chapter Ⅵ Generalized free products and HNN extensions
1. Applications = 103
2. Back to basics = 107
3. More applicatons = 111
4. Some word, conjugacy and isomorphism problems = 120
Chapter Ⅶ Groups acting on trees
1. Basic definitions = 123
2. Covering space theory = 129
3. Graphs of groups = 131
4. Trees = 134
5. The fundamental group of a graph of groups = 137
6. The fundamental group of a graph of groups(continued) = 139
7. Group actions and graphs of groups = 143
8. Universal covers = 147
9. The proof of Theorem 2 = 153
10. Some consequences of Theorem 2 and 3 = 154
11. The tree of SL2 = 158
Index = 163
