Metric Spaces of Non-Positive Curvature

• 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 fur Mathematik und ihre Grenzgebiete", 2002