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I am a very mathematically-oriented physicist. Since I never plan in making contact with "dirty" mechanics like robotics, structural problems or force diagrams, I want a book that prepares me for the mathematical/theoretical foundations of mechanics so that I can transition more smoothly to string theory and quantum field theory - where the action, the Hamilton-Jacobi equations and symmetries/Noether currents are in focus. Is there any book which "has it all" ?

I was wondering if someone could recommend me a CONCISE, preferably short, book which fulfils this in the language of differential geometry etc. An internet PDF would also be of interest...

Many thanks!