Refrence Request - Book for Manifolds over Banach Spaces

Question

Is there a book, other than Lang's, that treats the general theory of manifolds over Banach spaces?

Answer 1

Here are two suggestions, both available freely (and legally!) online:

• Richard Palais, Foundations of Global Non-Linear Analysis
• Richard Hamilton, The Inverse Function Theorem of Nash and Moser

Hamilton's monograph is really about Fréchet manifolds, which are more general than Banach manifolds, but his writing is spectacularly clear and he usually takes care to explain how things simplify when you're looking at Banach manifolds.

Answer 2

Many of the books by Mardsen and coauthors, e.g. "Manifold tensor analysis and applications" or "Foundation of Mechanics" develop most of the machinery over Banach spaces. I am not familiar with the books though, so you should check if they contain whatever specific you are looking for.