Differential geometry for nonlinear control theory 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.
 A: 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.
A: If you are still in search of a good reference, I would advise you the Agrachev & Sachkov "Control Theory from the Geometric Viewpoint". The book is quite useful for engineers like me and you, but you need a thorough read of first several chapters.
A: In case someone else in a search comes across this question. If you want to learn it for nonlinear control purposes, Nonlinear dynamical control systems by Nijmeijer and van der Schaft gives a nice introduction plus you clearly see where what is used, like Frobenius' theorem. Now if you what learn more about differential geometry I would suggest reading any book by John M. Lee, especially Introduction to Smooth Manifolds. Then If you want to continue, people like Jerrold Marsden, Hector Sussmann and Andrew Lewis all have fantastic material related to geometric control. Especially the book Manifolds, Tensor Analysis and Applications contains, I believe, close to all the mathematics related to control and dynamical systems, from a geometric point of view.  
