What is a good reference for rigorous Electromagnetism and Electrodynamics?

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.