TITLE: Self-contained book on Ricci Flow/Geometric Analysis
QUESTION [5 upvotes]: Can someone please tell me whether there is any self-contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self-contained I mean it does not assume that the reader is familiar with Analysis of PDE, rather quotes the required results and have a comprehensive appendix on PDE. I would appreciate if the book contained some exercises also.

REPLY [5 votes]: These books may also be the sort of thing you are after:

Peter Topping, Lectures on the Ricci flow
Ben Andrews and Christopher Hopper, Ricci Flow in Riemannian Geometry A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem

As Dean Yang pointed out in the comments above, being a PDE, the Ricci flow is, not surprisingly, studied by PDE methods. However, you can make a reasonable start far with only knowledge of the maximum principle (it's even described in Topping's book) if your are willing to assume existence/uniqueness. I think each book is fairly self-contained, and while many techniques used are PDE techniques, you can probably read them without knowing they apply to a broader range of PDE.