TITLE: Roadmap to learning about Ricci Flow?
QUESTION [23 upvotes]: Hello,
I'm curious to what books etc. one could use to understand the basics of Ricci flow, what areas of math are needed and so? What areas should one specialize in? See it as a roadmap to understanding Ricci flow, or something.Say one wants to be able to read Perelman's proof of the Poincaré Conjecture.
Sorry if my english isn't that good and this seems a bit hurried, I'm on the run.

REPLY [8 votes]: Here is a list of literature which I compiled when I taught the course
on Ricci flow.
Basic differential geometry:
Einstein Manifolds (Besse). 
Riemannian geometry (Gallot S., Hulin D., Lafontaine J.)
Sign and geometric meaning of curvature (Gromov)
http://www.ihes.fr/~gromov/PDF/1%5B77%5D.pdf
Textbooks:
Lectures on the Ricci Flow (2006, 133 pp.) Topping P.
http://www.warwick.ac.uk/~maseq/RFnotes.html 
Hamilton's Ricci Flow  (Chow B., Lu P., Ni L.)
Standard texts:
http://en.wikipedia.org/wiki/Solution_of_the_Poincar%C3%A9_conjecture
(and links therein)
Perelman, Grisha (November 11, 2002). 
The entropy formula for the Ricci flow and its geometric applications.
 Perelman, Grisha (March 10, 2003). 
Ricci flow with surgery on three-manifolds. 
Perelman, Grisha (July 17, 2003). 
Finite extinction time for the solutions to the 
Ricci flow on certain three-manifolds.  
Bruce Kleiner, John Lott.  Notes on Perelman's papers 
Huai-Dong Cao, Xi-Ping Zhu.  Hamilton-Perelman's Proof of
the Poincaré  Conjecture and the Geometrization Conjecture. 
John W. Morgan, Gang Tian.  
Ricci Flow and the Poincaré Conjecture

It's very obsolete (2007), and does not contain much on short-term
existence of solutions of Ricci flow.