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

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 other treatment of the theorem?

The theorem has been around for a long time.
So maybe they are some lecture note 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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