Is there any textbook (preferably not written by a physicist) on classical electrodynamics which gives a rigorous (by the standards of pure mathematics) treatment of (a part of) the topics found in the standard (nonrigorous) physics textbooks such as Jackson? (I don’t want to see anything like $\delta(x)$, the text should use distribution theory whenever necessary. Of course it is a shame that Bourbaki did not write such a thing.) Thanks a lot
Electromagnetic Theory and Computation A Topological Approach
by Paul W. Gross and P. Robert Kotiuga. Free in http://library.msri.org/books/Book48/.
Any book on differential gemoetry with gauge theory and bundles would probably do the job. Why don’t you have a look at Y. Choquet-Bruhat, C. DeWitt-Morette’s Analysis, Manifolds and Physics (both volumes)? In volume I, chapter Vbis (“Connections on a Principal Fibre Bundle”) classical electrodynamics is treated as gauge theory on certain fibre bundles.