Is there a textbook that explains Maxwell's equations in differential forms?

What I understood so far is that the $E$ and $B$ fields can be assembled to a 2-form $F$, and Maxwell's equations can be written quite nicely with the Hodge $*$ and the exterior deriative $d$. Going further the equations can be derived as Euler-Lagrange (or Yang-Mills?) equations from a connection of a fibre bundle.

I am searching for a book that describes how the geometric entities are mapped to the physical entities with a focus on mathematical exactness.

Discrete Cont. Dynam. Syst.,23(2009), pp 435-454. It treats also the nonlinear case. $\endgroup$ – Denis Serre Sep 25 '17 at 14:27