There are some well-known books on mathematical physics that are commonly used in undergraduate courses around the world as an introduction to mathematical methods in physics and/or applied sciences. My feeling about these mathematical physics books is that they are meant to be accessible to a large audience, i.e. physicists, engineers, mathematicians and so on. Thus, these books usually cover a lot of topics but most of them are poor in mathematical rigor. I'm looking for a book that cover these topics more rigorously, putting things in their context (functional analysis, linear algebra etc). As an example, I don't want to learn how to properly calculate the coefficients of a Fourier series but rather to learn that these series are expansions in terms of orthonormal basis in $L^{2}([0,1],\mathbb{R})$ and so on. What are some rigorous mathematical physics books?

Note: As I mentioned, I know that these courses on mathematical physics usually cover a lot of stuff and the best approach here would be to get a book for each subject. But I would like to know if there is some book which puts it all together, in the same way the classical books do, but in a more concrete and rigorous way.

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    $\begingroup$ Which part of mathematical physics are you talking about? Also what is your background? Without knowing the answer to both those questions it is impossible to give you any recommandation. Surely there is no single book that covers all of mathematical physics :) $\endgroup$ – Severin Schraven May 23 at 23:42

Reed and Simon, Methods of Modern Mathematical Physics. There are extensive "previews" in Google Books: I, II and a few more volumes.

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