TITLE: frechet manifolds book
QUESTION [8 upvotes]: hi, does anyone know a good book or some lecture notes on the theory of frechet manifolds ?

REPLY [11 votes]: 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.

REPLY [8 votes]: 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...