Differential Geometry

Intuitive

A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures by Jonathan Gratus

Concrete

Differential Geometry in Physics An introductory exposition for true non-experts by Marián Fecko
Differential Geometry and Lie Groups for Physicists by Marián Fecko
Manifolds and Differential Forms lecture notes by Reyer Sjamaar

Abstract

The motto in this section is: the higher the level of abstraction, the better.

Why is it interesting?