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.


Here are some references that might help:

Wikipedia page: https://en.wikipedia.org/wiki/Nash%E2%80%93Moser_theorem

"An Inverse Function Theorem in Frechet Spaces" by Ivar Ekeland: https://www.ceremade.dauphine.fr/~ekeland/Articles/InverseFunctionTheorem.pdf

"On the Nash-Moser Implicit Function Theorem" by Lars Hormander: http://www.acadsci.fi/mathematica/Vol10/vol10pp255-259.pdf

"The Implicit Function Theorem; History, Theory, and Application" by Steven Krantz and Harold Parks: https://books.google.co.uk/books?id=7QqickY0yh8C&pg=PA135&lpg=PA135&dq=nash+moser+implicit+function+theorem&source=bl&ots=Ucsqm-INvv&sig=Sg4SuE3zDDwDBCD8L_y-635iL8o&hl=en&sa=X&ei=xZiXVceGF4us7AbQ4JK4Aw&ved=0CGMQ6AEwCQ#v=onepage&q=nash%20moser%20implicit%20function%20theorem&f=false

"Pseudo-Differential Operators and the Nash-Moser Theorem" by Serge Alinhac and Patrick Gerard: https://books.google.co.uk/books?id=GQAPCgAAQBAJ&pg=PA145&lpg=PA145&dq=nash+moser+theorem&source=bl&ots=upjExN46hK&sig=X_FWca2gHwefgzUfrxwe7l1xzCI&hl=en&sa=X&ved=0CFkQ6AEwDDgKahUKEwit6r6W9OTGAhVhgdsKHXRWB5I#v=onepage&q=nash%20moser%20theorem&f=false