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 Mathematical Surveys and Monographs 2014; 594 pp; hardcover Volume: 196 ISBN-10: 1-4704-1456-2 ISBN-13: 978-1-4704-1456-6 List Price: US$134 Member Price: US$107.20 Order Code: SURV/196 Not yet published.Expected publication date is April 15, 2014. See also: Geometric Nonlinear Functional Analysis: Volume 1 - Yoav Benyamini and Joram Lindenstrauss The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years. Readership Graduate students and research mathematicians interested in geometric and analytic study of convex bodies.