The goal of this book is to present several central topics in geometric group theory, primarily related to the large scale geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as Gromov’s Theorem on groups of polynomial growth. Topics covered includes: Geometry and Topology, Metric spaces, Differential geometry, Hyperbolic Space, Groups and their actions, Median spaces and spaces with measured walls, Finitely generated and finitely presented groups, Coarse geometry, Coarse topology, Geometric aspects of solvable groups, Gromov’s Theorem, Amenability and paradoxical decomposition, Proof of Stallings’ Theorem using harmonic functions.

Cornelia Drutu and Michael Kapovich