The two main textbooks for this course are Differentiable Manifolds. A First Course by Lawrence Conlon, Birkhäuser Advanced Texts, Basler Lehrebücher, Birkhäuser (1993) and Introduction to differential topology by Th. Brocker and K. Jänich, Cambridge University Press (1982). To see the Birkhäuser's catalogue entry for Conlon's book (with its table of contents cilck on it). Brocker and Jänich is out-of-print now but I will try to arrange that you get a copy. The lectures will cover the following topics:
- Topological manifolds
- Manifolds and differentiable structures
- Tangent bundle
- Vector bundles and multilinear algebra
- Submanifolds, immersions, and embeddings
- Vector fields, flows, and foliations
- Lie groups, principal bundles, and homogeneous spaces
- Covectors and smooth p-forms
- Integration and cohomology
- Forms and foliations
- Symplectic manifolds
- Riemannian manifolds