This third edition is addressed to the mathematician or graduate student of mathematics - or
even the well-prepared undergraduate - who would like with a minimum of background and
preparation to understand some of the beautiful results at the heart of nonlinear analysis.
Based on carefully-expounded ideas from several branches of topology and illustrated by a
wealth of figures that attest to the geometric nature of the exposition the book will be of
immense help in providing its readers with an understanding of the mathematics of the nonlinear
phenomena that characterize our real world. Included in this new edition are several new
chapters that present the fixed point index and its applications. The exposition and
mathematical content is improved throughout. This book is ideal for self-study for
mathematicians and students interested in such areas of geometric and algebraic topology
functional analysis differential equations and applied mathematics. It is a sharply focused
and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear
path to understanding. For the topology-minded reader the book indeed has a lot to offer:
written in a very personal eloquent and instructive style it makes one of the highlights of
nonlinear analysis accessible to a wide audience.-Monatshefte fur Mathematik (2006)
