What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for something that would include E&M in the big picture of Gauge theories.

Solution 1:

Here are a couple of books that aren't necessarily meant for mathematicians but are pretty mathematical:

Foundations of Classical Electrodynamics: Charge, Flux, and Metric by Friedrich W. Hehl and Yuri N. Obukhov. This book is probably closest to what you're looking for. It is very rigorous, even starting by stating a set of axioms for classical electrodynamics. This book not only uses differential forms, but tensors in their full(ish) glory.
Gauge Fields, Knots & Gravity by John Baez and Javier P. Muniain. This book is specifically about gauge fields and classical field theory. The first third of the book is on E&M and is an introduction to differential forms and de Rham theory.

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