The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories. Many recent rather deep theorems and delicate examples are included with complete and detailed proofs. Challenging open problems are described and explained, and promising new research directions are indicated. Readership Graduate students and research mathematicians interested in functional analysis; theoretical computer scientists. Reviews "Important monograph, written by leading specialists in the field ... notes and remarks ... contain interesting historical notes and information about a vast amount of related results ... Challenging open problems are described and explained. The vast majority of the material appears for the first time in book form, and many quite recent deep results are proved."  European Mathematical Society Newsletter "Much ... is explained in this book in a splendid and fascinating way. The considerable amount of mathematics is divided into seventeen chapters which are essentially independent. Three or four of them chosen adlibitum would provide an excellent basis for a graduate course ... researchers will enjoy this invitation to the deepest parts of functional analysis."  Mathematical Reviews "Without any doubt, this is one of the great books on nonlinear analysis which will certainly become a standard reference. It is not only a must for every math library all over the world, but also for all researchers interested in functional analysis, operator theory, geometry of Banach spaces, and nonlinear problems."  Zentralblatt MATH Table of Contents  Introduction
 Retractions, extensions and selections
 Retractions, extensions and selections (special topics)
 Fixed points
 Differentiation of convex functions
 The RadonNikodým property
 Negligible sets and Gâteaux differentiability
 Lipschitz classification of Banach spaces
 Uniform embeddings into Hilbert space
 Uniform classification of spheres
 Uniform classification of Banach spaces
 Nonlinear quotient maps
 Oscillation of uniformly continuous functions on unit spheres of finitedimensional subspaces
 Oscillation of uniformly continuous functions on unit spheres of infinitedimensional subspaces
 Perturbations of local isometries
 Perturbations of global isometries
 Twisted sums
 Group structure on Banach spaces
 Appendices
 Bibliography
 Index
