The main theme of the book is the nonlinear geometry of Banach spaces, and it considers various significant problems in the field. The present book is a commented transcript of the notes of the graduate-level topics course in nonlinear functional analysis given by the late Nigel Kalton in 2008. Nonlinear geometry of Banach spaces is a very active area of research with connections to theoretical computer science, noncommutative geometry, as well as geometric group theory and Nigel Kalton was the most influential and prolific contributor to the theory. Collected here are the topics that Nigel Kalton felt were significant for those first dipping a toe into the subject of nonlinear functional analysis and presents these topics in an accessible and concise manner. As well as covering some well-known topics, it also includes recent results discovered by Kalton and his collaborators which have not previously appeared in textbook form. A typical first-year course in functional analysis will provide sufficient background for readers of this book.
