From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2

Table of Contents

1 Fake R4

2 The Yang-Mills Equations

3 Manifolds of Connections

4 Cones on CIFD2

5 Orientability

6 Introduction to Taubes' Theorem

7 Taubes' Theorem

8 Compactness

9 The Collar Theorem

10 The Technique of Fintushel and Stem