I. Geodesic Metric Spaces.- 1. Basic Concepts.- 2. The Model Spaces M?n.- 3. Length Spaces.- 4. Normed Spaces.- 5. Some Basic Constructions.- 6. More on the Geometry of M?n.- 7. M?-Polyhedral Complexes.- 8. Group Actions and Quasi-Isometries.- II. CAT(?) Spaces.- 1. Definitions and Characterizations of CAT(?) Spaces.- 2. Convexity and Its Consequences.- 3. Angles, Limits, Cones and Joins.- 4. The Cartan-Hadamard Theorem.- 5. M?-Polyhedral Complexes of Bounded Curvature.- 6. Isometries of CAT(0) Spaces.- 7. The Flat Torus Theorem.- 8. The Boundary at Infinity of a CAT(0) Space.- 9. The Tits Metric and Visibility Spaces.- 10. Symmetric Spaces.- 11. Gluing Constructions.- 12. Simple Complexes of Groups.- III. Aspects of the Geometry of Group Actions.- H. ?-Hyperbolic Spaces.- ?. Non-Positive Curvature and Group Theory.- C. Complexes of Groups.- G. Groupoids of local Isometries.- References.
"This book is beautifully and clearly written and contains many
illustrations and examples but also many deep results.
It is my opinion that this book will become a standard work in
mathematical literature and will be used by many people, from
undergraduates to specialists."
K. Dekimpe in "Nieuw Archief voor Wiskunde", June 2001 "In
conclusion, it can be said that the book is an indispensable
reference and a very useful tool for graduate students who want to
learn this theory as well as for researchers working in the
subject. The exposition is clear, the proofs are complete, and some
of the advanced results that are discussed are original. Every
section of the book contains interesting historical remarks and
comments." A. Papadopoulos in "Zentralblatt für Mathematik und ihre
Grenzgebiete", 2002
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