Introduction to Differential Topology

• Preface; 1. Manifolds and differentiable structures; 2. Tangent space; 3. Vector bundles; 4. Linear algebra for vector bundles; 5. Local and tangential properties; 6. Sard's theorem; 7. Embedding; 8. Dynamical systems; 9. Isotopy of embeddings; 10. Connected sums; 11. Second order differential equations and sprays; 12. The exponential map and tubular neighbourhoods; 13. Manifolds with boundary; 14. Transversality; References; Index of symbols; Subject index.

'The book of Brocker and Janich is the best introduction to elementary differential topology that I know. It is recommended wholeheartedly to every student for self-study and can also serve well as the foundation for an introductory course on differentiable manifolds.' E. Brieskorn, Jahresberichte der Deutsche Mathematische Vereinigung