The semester here in Bonn just ended, which means that the topics course I have been teaching has come to an end. It ended up being about two things. The first half was about approximations of functions. We proved the smooth approximation theorems and Jet transversality theorems. With this we were abel to prove the Whitney embedding and immersion theorems as well as the Pontryagin-Thom construction.
In the second half of the course we covered the h-principle including the proof that the sheaf of solutions to any open partial differential relation satisfies the h-principle for any open manifold. This includes sheaves of immersions, submersions, Morse functions, and many others.
The course notes can be found here.