双曲几何讲义（英文）

The Hyperbolic Geometry Lectures is a book that delves into the study of hyperbolic manifolds. The main theme of the book is the conflict between the flexibility and rigidity properties of hyperbolic manifolds. The book explores the differences between dimension 2 and higher dimensions and proves this in chapters B and C. An elementary feature of this phenomenon is the difference between the Riemann mapping theorem and Liouville's theorem, as pointed out in chapter A. This introductory chapter is quite accessible and most of its material may be the object of an undergraduate course.In addition to the rigidity theorem, Margulis' Lemma is also discussed in chapter D. The book gives a detailed proof of this result and as a consequence, a rather accurate description of the thin-thick decomposition of a hyperbolic manifold is provided in chapter D as well. This information is especially useful in case of finite volume.This book is a must-read for those interested in geometry and topology. The way the author presents the material is clear and concise, making it accessible even for those who may not have much background in the subject. The examples and illustrations provided also aid in helping the reader understand the concepts presented in the book. Overall, the Hyperbolic Geometry Lectures is a valuable resource for anyone interested in the study of hyperbolic manifolds.