TITLE: Infinite dimensional Riemannian geometry
QUESTION [9 upvotes]: My current research has brought me into an area the requires me to learn some infinite dimensional Riemannian and Kähler geometry. Can someone recommend some good books or survey articles to help me get started with the basics? I've seen Lang's book but that's it.

REPLY [4 votes]: I would also  suggest the beautiful paper by Arnold 
http://www.ams.org/mathscinet-getitem?mr=202082
and the book by 
Kriegl-Michor: The convenient setting of global analysis, 
see also the references therein.