Acknowledgements
1. Introduction
2. The Euler class and obstruction theory
3. Spherical fibrations
4. Stable cohomotopy
5. Framed manifolds
A. Appendix: on the Hopf variant
6. K-theory
7. The image of J
8. The Euler characteristic
9. Topological Hermitian K-theory
10. Algebraic Hermitian K-theory
B. Appendix: on the Hermitian J-homomorphism
Bibliography
Index.

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