Functional Differential Geometry by Sussman, Wisom, and Farr in 2013
1. Introduction
2. Manifolds
4. Basis fields
5. Integration
6. Over a map
7. Directional derivatives
8. Curvature
9. Metrics
10. Hodge star and electrodynamics
11. Special relativity
A. Scheme
B. Our notation
C. Tensors