| |
| |
| Introduction | |
| |
| |
| |
| Gauss' circle problem and Polya's random walks on lattices | |
| |
| |
| |
| The circle problem | |
| |
| |
| |
| Polya's recurrence theorem | |
| |
| |
| |
| Free products and free groups | |
| |
| |
| |
| Free Products of Groups | |
| |
| |
| |
| The Table-Tennis Lemma (Klein's criterion) and examples of free products | |
| |
| |
| |
| Finitely-generated groups | |
| |
| |
| |
| Finitely-generated and infinitely-generated groups | |
| |
| |
| |
| Uncountably many groups with two generators (B.H. Neumann's method) | |
| |
| |
| |
| On groups with two generators | |
| |
| |
| |
| On finite quotients of the modular group | |
| |
| |
| |
| Finitely-generated groups viewed as metric spaces | |
| |
| |
| |
| Word lengths and Cayley graphs | |
| |
| |
| |
| Quasi-isometries | |
| |
| |
| |
| Finitely-presented groups | |
| |
| |
| |
| Finitely-presented groups | |
| |
| |
| |
| The Poincare theorem on fundamental polygons | |
| |
| |
| |
| On fundamental groups and curvature in Riemannian geometry | |
| |
| |
| |
| Complement on Gromov's hyperbolic groups | |
| |
| |
| |
| Growth of finitely-generated groups | |
| |
| |
| |
| Growth functions and growth series of groups | |
| |
| |
| |
| Generalities on growth types | |
| |
| |
| |
| Exponential growth rate and entropy | |
| |
| |
| |
| Groups of exponential or polynomial growth | |
| |
| |
| |
| On groups of exponential growth | |
| |
| |
| |
| On uniformly exponential growth | |
| |
| |
| |
| On groups of polynomial growth | |
| |
| |
| |
| Complement on other kinds of growth | |
| |
| |
| |
| The first Grigorchuk group | |
| |
| |
| |
| Rooted d-ary trees and their automorphisms | |
| |
| |
| |
| The group [Gamma] as an answer to one of Burnside's problems | |
| |
| |
| |
| On some subgroups of [Gamma] | |
| |
| |
| |
| Congruence subgroups | |
| |
| |
| |
| Word problem and non-existence of finite presentations | |
| |
| |
| |
| Growth | |
| |
| |
| |
| Exercises and complements | |
| |
| |
| References | |
| |
| |
| Index of research problems | |
| |
| |
| Subject index | |