Dear Toussaint, Frankel has written a book whose very title *The geometry of physics: an introduction*  makes me think it might be what you want. The second paragraph of the introduction  confirms this impression:*This is a textbook that develops some of the geometrical concepts and tools that
are helpful in understanding classical and modem physics and engineering.* (the last word will warm your heart!)

Tensors and exterior products, for example, are presented in a very concrete way, without introducing more abstract concepts like quotients of free modules. And the pictures are numerous and very evocative.         
Google will let you browse [the book] [1]

**To mathematicians** Like many of us, I have a melanchcoly love for physics from my student days and I find this book written in exactly the right language for a mathematician wanting to (re)learn some physics (the title doesn't say it but there is quite a bit of physics in this book) 




[1]:http://books.google.fr/books?id=DUnjs6nEn8wC&printsec=frontcover&dq=Frankel+the+geometry+of+physics&hl=fr&ei=wASiTaLYMNGv8QO60OWoAw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDQQ6AEwAA#v=onepage&q&f=false