*Frontmatter, pg. i*CONTENTS, pg. v*INTRODUCTION, pg. ix*CHAPTER 1. CLASSIFYING SPACES AND COBORDISM, pg. 1*CHAPTER 2. THE SURGERY CLASSIFICATION OF MANIFOLDS, pg. 29*CHAPTER 3. THE SPACES SG AND BSG, pg. 45*CHAPTER 4. THE HOMOTOPY STRUCTURE OF G/PL AND G/TOP, pg. 76*CHAPTER 5. THE HOMOTOPY STRUCTURE OF MSPL[1/2] AND MSTOP[1/2], pg. 99*CHAPTER 6 . INFINITE LOOP SPACES AND THEIR HOMOLOGY OPERATIONS, pg. 124*CHAPTER 7. THE 2-LOCAL STRUCTURE OF B(G/TOP), pg. 141*CHAPTER 8 . THE TORSION FREE STRUCTURE OF THE ORIENTED COBORDISM RINGS, pg. 158*CHAPTER 9. THE TORSION FREE COHOMOLOGY OF G/TOP AND G/PL, pg. 174*CHAPTER 10. THE TORSION FREE COHOMOLOGY OF BTOP AND BPL, pg. 193*CHAPTER 11. INTEGRALITY THEOREMS, pg. 209*CHAPTER 12. THE SMOOTH SURGERY CLASSES AND H*(BTOP; Z/2), pg. 223*CHAPTER 13. THE BOCKSTEIN SPECTRAL SEQUENCE FOR BTOP, pg. 235*CHAPTER 14. THE TYPES OF TORSION GENERATORS, pg. 246*APPENDIX. THE PROOFS OF 13.12, 13.13, AND 13.15, pg. 256*BIBLIOGRAPHY, pg. 263*INDEX, pg. 274*Backmatter, pg. 280