I'm looking for a good source for a large collection of Differential Manifolds/Geometry questions covering a subset of the following topics:
inverse function theorem, local coordinates, induced structures, tangent bundle, regular values, transversality, classical Lie groups, tubular neighborhoods, vector fields and flows, differential forms and de Rham cohomology, integration of forms and Stokes Theorem, relationship to singular homology, de Rham theorem, Riemannian metrics.
Multiple sources are welcome. I do have access to A Comprehensive Introduction to Differential Geometry by Spivak and Topology and Geometry by Bredon. Does anyone else know where I can find more questions? I am particularly interested in concrete problems concerning specific manifolds.
In fact, if there is a text available that teaches geometry by deeply dissecting a large collection of examples I would be very appreciative.