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To learn, the Nash-Moser implicit function theorem, I tried the document

Hamilton (1982) The Inverse Function Theorem of Nash and Moser,

but the article is very encyclopedic. I have a background in functional analysis, but not in differential geometry so I often lost the main idea of the text.

I will try with the original article of Nash and Moser.

Are there any other treatments of the theorem?

The theorem has been around for a long time, so maybe they are some lecture notes or book which expose it with less sophistication than Hamilton.

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You could try the short treatment (4 rather dense pages) of a version of this theorem by K. Asano here. – Bob Pego Oct 30 '13 at 2:40

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