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up vote 6 down vote accepted

There is the book by Kriegl and Michor called "Convenient setting of global analysis" published by the AMS. It goes much beyond Fréchet and really gives a big panorama. However, it is not easy reading and requires really some work. But I guess that is due to the subject...

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Also worth noting that it can be downloaded for free from the AMS bookstore. – Loop Space Sep 8 '11 at 8:43
@Andrew: yes that's nice. In fact, a lot of the marvelous books by Michor are available for free on his homepage. It's worth looking at... – Stefan Waldmann Sep 8 '11 at 8:49

You could try

Hamilton, Richard S. (1982). "The inverse function theorem of Nash and Moser". Bull. Amer. Math. Soc. (N.S.) 7 (1): 65–222. doi:10.1090/S0273-0979-1982-15004-2

And there's a paper by Milnor on infinite dimensional Lie groups which could be useful.

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It is available for free here:… – David Roberts May 28 '12 at 1:51

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