Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz's global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of NashMoser type with applications to KolmogorovArnoldMoser theory and to conjugacy problems. After more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University. Readership Graduate students and research mathematicians interested in functional analysis. Reviews "This is the second edition of the wellknown and remarkable book on nonlinear analysis ... The book is useful for all specialists in nonlinear analysis, first for young mathematicians that, due to this book, can become acquainted with a series of fundamental and brilliant ideas and methods of nonlinear analysis."  Zentralblatt MATH From reviews for the First Edition: "These lecture notes are extremely stimulating."  Zentralblatt MATH "[The book] is short, concise, and to the point, and the proofs are unusually elegant, always with a geometric flavor and the best available."  Mathematical Reviews Table of Contents  Topological approach: Finite dimensions
 Topological degree in Banach space
 Bifurcation theory
 Further topological methods
 Monotone operators and the minmax theorem
 Generalized implicit function theorems
 Bibliography
