Contents EDITOR'S PREFACE v PREFACE vii 1. ALGEBRAIC CONSTRUCTIONS 1 2. HOMOTOPY THEORETICAL LOCALIZATION 31 3. COMPLETIONS IN HOMOTOPY THEORY 51 4. SPHERICAL FIBRATIONS 89 5. ALGEBRAIC GEOMETRY 113 6. THE GALOIS GROUP IN GEOMETRIC TOPOLOGY 187 REFERENCES 241 GALOIS SYMMETRY IN MANIFOLD THEORY AT THE PRIMES Reprint from Proc. 1970 Nice ICM 251 POSTSCRIPT(2004) 261