I am an engineering student and I need to acquire a good understanding of some notions in differential geometry such as manifolds, diffeomorphisms, distributions, etc. I can't find a proper starting path. How should I start to learn the subject from basics?
I need the material to study geometric nonlinear control theory. Any further suggestions are appreciated.
I would suggest you to start with Isidori's Nonlinear Control I. The book contains the basic theory of differential geometry needed for nonlinear control. In case you need more information regarding differential geometry, take a look at Boothby's Differential Geometry.