For those into physics, I wholeheartedly recommend Marsden and Ratiu's book, "Introduction to Mechanics and Symmetry", which deals mainly with the different formulations of physics applied to symplectic and associated geometries.
Thanks for the recommendation! I didn't know this one. I try and lap up everything I can by Marsden, (though more often through the lens of applied researchers: e.g. Desbrun, Hirani, Crane, and others -- much involving computer graphics and/or discrete differential geometry applied to physical simulation. In short, I better say that I am not familiar with the scope of Marsden's work. I am sure much of it is beyond me, but gosh darned it, the exterior calculus is beautiful and these guys write brilliantly readable stuff for an engineer.
Even as a hydrodynamics software guy, I found the computer graphics research community to be the easiest entry-point for, especially, the topology and modern differential geometry. It's especially nice when they do a simulation paper with a high end geometric/analytic approach.
This might be a good place to go in order to have a start at, say, Arnold's ``topological methods in hydrodynamics'' or anything TQFT-esque.
