*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii* 1. Smooth Manifolds, pg. 1* 2. Vector Bundles, pg. 13* 3. Constructing New Vector Bundles Out of Old, pg. 25* 4. Stiefel-Whitney Classes, pg. 37* 5. Grassmann Manifolds and Universal Bundles, pg. 55* 6. A Cell Structure for Grassmann Manifolds, pg. 73* 7. The Cohomology Ring H*(Gn; Z/2), pg. 83* 8. Existence of Stiefel-Whitney Classes, pg. 89* 9. Oriented Bundles and the Euler Class, pg. 95* 10. The Thom Isomorphism Theorem, pg. 105* 11. Computations in a Smooth Manifold, pg. 115* 12. Obstructions, pg. 139* 13. Complex Vector Bundles and Complex Manifolds, pg. 149* 14. Chern Classes, pg. 155* 15. Pontrjagin Classes, pg. 173* 16. Chern Numbers and Pontrjagin Numbers, pg. 183* 17. The Oriented Cobordism Ring OMEGA*, pg. 199* 18. Thom Spaces and Transversality, pg. 205* 19. Multiplicative Sequences and the Signature Theorem, pg. 219* 20. Combinatorial Pontrjagin Classes, pg. 231*Epilogue, pg. 249*Appendix A: Singular Homology and Cohomology, pg. 257*Appendix B: Bernoulli Numbers, pg. 281*Appendix C: Connections, Curvature, and Characteristic Classes, pg. 289*Bibliography, pg. 315*Index, pg. 325
