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.