IRMA Lectures in Mathematics and Theoretical Physics 2013; 320 pp; softcover Volume: 6 ISBN10: 3037191325 ISBN13: 9783037191323 List Price: US$58 Member Price: US$46.40 Order Code: EMSILMTP/6.R
 This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. The book also contains a systematic introduction to metric geometry, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature. The concepts and the techniques are illustrated by many examples, in particular from hyperbolic geometry, Hilbert geometry and Teichmüller theory. For the second edition, some corrections and a few additions have been made, and the bibliography has been updated. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in geometry, topology, and analysis. Table of Contents  Introduction: Some historical markers
 Lengths of paths in metric spaces
 Length spaces and geodesic spaces
 Maps between metric spaces
 Distances
 Convexity in vector spaces
 Convex functions
 Strictly convex normed vector spaces
 Busemann spaces
 Locally convex spaces
 Asymptotic rays and the visual boundary
 Isometries
 Busemann functions, corays and horospheres
 Bibliography
 Index
