Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 Cayley's Theorems -- 1.1 Cayley's Basic Theorem -- 1.2 Graphs -- 1.3 Symmetry Groups of Graphs -- 1.4 Orbits and Stabilizers -- 1.5 Generating Sets and Cayley Graphs -- 1.5.1 Generators -- 1.5.2 Cayley's Better Theorem -- 1.6 More Cayley Graphs -- 1.6.1 Dihedral Groups -- 1.6.2 Symmetric Groups -- 1.6.3 The Symmetry Group of a Cube -- 1.6.4 Free Abelian Groups -- 1.7 Symmetries of Cayley Graphs -- 1.8 Fundamental Domains and Generating Sets -- 1.9 Words and Paths -- Exercises -- 2 Groups Generated by Reflections -- Exercises -- 3 Groups Acting on Trees -- 3.1 Free Groups -- 3.1.1 Free Groups of Rank n -- 3.1.2 F2 as a Group of Tree Symmetries -- 3.1.3 Free Groups in Nature -- 3.2 F3 is a Subgroup of F2 -- 3.3 Free Group Homomorphisms and Group Presentations -- 3.4 Free Groups and Actions on Trees -- 3.5 The Group Z3 * Z4 -- 3.6 Free Products of Groups -- 3.7 Free Products of Finite Groups are Virtually Free -- 3.8 A Geometric View of Theorem 3.35 -- 3.9 Finite Groups Acting on Trees -- 3.10 Serre's Property FA and Infinite Groups -- Exercises -- 4 Baumslag-Solitar Groups -- Exercises -- 5 Words and Dehn's Word Problem -- 5.1 Normal Forms -- 5.2 Dehn's Word Problem -- 5.3 The Word Problem and Cayley Graphs -- 5.4 The Cayley Graph of BS(1,2) -- Exercises -- 6 A Finitely Generated, Infinite Torsion Group -- Exercises -- 7 Regular Languages and Normal Forms -- 7.1 Regular Languages and Automata -- 7.2 Not All Languages are Regular -- 7.3 Regular Word Problem? -- 7.4 A Return to Normal Forms -- 7.5 Finitely Generated Subgroups of Free Groups -- Exercises -- 8 The Lamplighter Group -- Exercises -- 9 The Geometry of Infinite Groups -- 9.1 Gromov's Corollary, aka the Word Metric -- 9.2 The Growth of Groups, I -- 9.3 Growth and Regular Languages -- 9.4 Cannon Pairs.

9.5 Cannon's Almost Convexity -- Exercises -- 10 Thompson's Group -- Exercises -- 11 The Large-Scale Geometry of Groups -- 11.1 Changing Generators -- 11.2 The Growth of Groups, II -- 11.3 The Growth of Thompson's Group -- 11.4 The Ends of Groups -- 11.5 The Freudenthal-Hopf Theorem -- 11.6 Two-Ended Groups -- 11.7 Commensurable Groups and Quasi-Isometry -- Exercises -- Bibliography -- Index.