This book is based on a series of post-doctoral level lectures given at

Université Paris-Est Marne-la-Vallée in November 2009, by Djalil Chafaï,

Olivier Guédon, Guillaume Lecué, Shahar Mendelson, and Alain Pajor.

It aims to bridge several actively developed domains of research around

high dimensional phenomena and asymptotic geometric analysis. The

covered topics include empirical methods and high dimensional geometry,

concentration of measure, compressed sensing, Gelfand widths, chaining

methods, singular values, Wishart matrices, and problems of selection of

characters. This book focuses on methods and concepts. Chapters are

mostly self-contained. An index is provided.