To get an intuitive understanding of the Stokes theorem, I recommand the book by Arnol'd on mechanics. It gives a very intuitive definition of the exterior derivative in such a way that the Stokes theorem becomes, heuristically, very easy to grasp.

I also find "Analysis, manifolds and physics" (books.google.com/books?id=hUWEXphqLo8C) and "Geometry, topology and physics" (books.google.com/books?id=cH-XQB0Ex5wC) to be two great source of inspiration to understand the intertwining between geometry and physics. The first is written by mathematicians, the second by a physicist.

PS. Absurdly, I can only post one hyperlink in that answer... 8-(

To get an intuitive understanding of the Stokes theorem, I recommand the book by Arnol'd on mechanics. It gives a very intuitive definition of the exterior derivative in such a way that the Stokes theorem becomes, heuristically, very easy to grasp.

I also find Analysis, manifolds and physics and Geometry, topology and physics to be two great source of inspiration to understand the intertwining between geometry and physics. The first is written by mathematicians, the second by a physicist.