几何群论是指利用拓扑、几何、动力学和分析工具研究离散群的学科。这一领域发展非常迅速，本书对在这一发展中起关键作用的各种主题进行了介绍和概述。
本书包含了Park City Math lnstitute关于几何群论的课程讲义。该研究所由该领域的领袖级专家提供一系列密集的短期课程，旨在向学生介绍数学领域中令人兴奋的最新研究。这些讲座不重复其他地方提供的标准课程。这些课程从适合研究生的入门级别开始，一直引领到目前正在活跃的研究课题。本书中的文章包括对CAT（O）立方复形和群、现代小消去理论、一般CAT（O）空间的等距群的介绍，以及在映射类群和CAT（O）群的背景下讨论幂零亏格。一门课程概述了准等距刚性，其他课程包括探索外层空间的几何学、算术群的作用、格和局部对称空间、标记长度谱和扩展图、tau性质和近似群。
本书为对几何群论感兴趣的研究生和研究人员提供了一份有价值的资源。

Preface
Mladen Bestvina, Michah Sageev, Karen Vogtmann Introduction
Michah Sageev
CAT(0) Cube Complexes and Groups
Introduction
Lecture 1. CAT(0) cube complexes and pocsets
1. The basics of NPC and CAT(0) complexes
2. Hyperplanes
3. The pocset structure
Lecture 2. Cubulations: from pocsets to CAT(0) cube complexes
1. Ultrafilters
2. Constructing the complex from a pocset
3. Examples of cubulations
4. Cocompactness and properness
5. Roller duality
Lecture 3. Rank rigidity
1. Essential cores
2. Skewering
3. Single skewering
4. Flipping
5. Double skewering
6. Hyperplanes in sectors
7. Proving rank rigidity
Lecture 4. Special cube complexes
1. Subgroup separability
2. Warmup-Stallings' proof of Marshall Hall's theorem
3. Special cube complexes
4. Canonical completion and retraction
5. Application: separability of quasiconvex subgroups
6. Hyperbolic cube complexes are virtually special
Bibliography
Vincent Guirardel
Geometric Small Cancellation
Introduction
Lecture 1. What is small cancellation about?
1. The basic setting
2. Applications of small cancellation
3. Geometric small cancellation
Lecture 2. Applying the small cancellation theorem
1. When the theorem does not apply
2. Weak proper discontinuity
3. SQ-universality
4. Dehn fillings
Lecture 3. Rotating families
1. Road-map of the proof of the small caamcellation theorem
2. Definitions
3. Statements
4. Proof of Theorem 3.4
5. Hyperbolicity of the quotient
6. Exercises
Lecture 4. The cone-off
1. Presentation
2. The hyperbolic cone of a graph
3. Cone-off of a space over a family of sulepaces
Bibliography
Pierre-Emmanuel Caprace
Lectures on Proper CAT(0) Spaces and Their Isometry Groups
Introduction
Lecture 1. Leading examples
1. The basics
2. The Cartan-Hadamard theorem
3. Proper cocompact spaces
4. Symmetric spaces
5. Euclidean buildings
6. Rigidity
7. Exercises
Lecture 2. Geometric density
1. A geometric relative of Zariski density
2. The visual boundary
3. Convexity
4. A product decomposition theorem
5. Geometric density of normal subgroups
6. Exercises
……
Michael Kapovich
Lectures on Quasi-Isometric Rigidity
Mladen Bestvina
Geometry of Outer Space
Dave Witte Morris
Some Arithmetic Groups that Do Not Act on the Circle
Tsachik Gelander
Lectures on Lattices and Locally Symmetric Spaces
Amie Wilkinson
Lectures on Marked Length Spectrum Rigidity
Emmanuel Breuillard
Expander Graphs, Property (T) and Approximate Groups
Martin R. Bridson
Cube Complexes, Subgroups of Mapping Class Groups, and Nilpotent Genus