Sean Carroll's Lecture Notes on General Relativity contain a superb introduction to the mathematics of GR (differential geometry on Riemann manifolds). These also also published in modified form in his book, Spacetime and Geometry.

Spivak's Calculus on Manifolds is a gem.

Bishop's Tensor Analysis on Manifolds is a great introduction to the subject, and published by Dover, is very cheap (less than $10 on amazon).

Georgi's Lie Algebras In Particle Physics is enjoyable and fast-paced, but probably skips around too much to be used as an adequate first exposure.

Shutz's Geometrical Methods of Mathematical Physics and A First Course in General Relativity.

Despite it's incredibly pompous title, Penrose's The Road to Reality: A Complete Guide to the Laws of the Universe provides an enjoyable high-level view of a vast expanse of mathematical physics.

As mentioned by Cedric, I am a huge fan of Sussman and Wisdom's Structure and Interpretation of Classical Mechanics and the associated Functional Differential Geometry memo. The citations in those publications will also point to towards a lot of good material and there's more goodies if you dig around in the source code.