Includes Indexes

Includes bibliography (pages 323-354) and references.

Euclidean sections
Separable Banach spaces without the approximation property
Gaussian processes
Reflexive subspaces of L1
The method of selectors: examples of its use
The Pisier space of almost surely continuous functions: applications
News in the theory of infinite-dimensional Banach spaces in the past twenty years
An update on problems in high-dimensional convex geometry and related probabilistic results
A few updates and pointers
On the mesh condition for Sidon sets

This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition

Originally published in French as Introduction à l'étude des espaces de Banach by Société Mathématique de France, 2004