Which road to Special and General Relativity, and beyond?

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Hello, I am studying mathematics and physics on my own. However, it is the mathematical side of physics that intrest me.

I would like some recommendations on which books would be beneficial for me to read, to gain an understanding of Special and General Relativity, and ultimatly string theory.

I am currently reading Calculus by M. Spivak, and Linear Algebra Done Right, by S. Axler.
If anyone could suggest books to read after I'm done with these, I would be greateful.

.. Mads
 
Those are very good books. Two books I'd suggest that cover Multi-variable calculus and ODE at the level of Axler and Spivak (read high) are:

Analysis on Manifolds - Munkres
Ordinary Differential Equations - V. Arnold (note I'd get the "new" edition as it covers the standard solution methods as well as the dynamical systems stuff)

Both books are difficult but not harder then Spivak or Axler in my opinion.

I think it might be best to cover a little more math and physics before tackling General Relavity but Special Relativity is a very accessible subject. I's suggest "Spacetime Physics" its a good introduction but I'd say its the easiest book I've recommended.
 
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Hi Deluks, thank you very much for your suggestions! The books you suggested does indeed seem excellent.

.. Mads
 

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