This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces.  This new material is intended to present  these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them.

Fernando Albiac is Professor of mathematical analysis at the Public University of Navarra in Pamplona Spain. His current research focuses primarily on geometric nonlinear functional analysis and greedy approximation with respect to bases in Banach spaces.

Nigel Kalton was Professor of Mathematics at the University of Missouri, Columbia. He wrote over 250 articles with nearly 100 different co-authors, and was the recipient of the 2004 Banach Medal of the Polish Academy of Sciences.