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