I started to read the book "The Poincare Conjecture In Search of The Shape of The Universe." It is a terrific book that explains the history of Poincare's conjecture in layman terms. The book changed the way that I visualize mathematics. I was wondering what is the mathematical background that is needed in order to be able to study and to understand The Ricci Flow? Appart from advanced calculus, real/complex analysis, PDE, Riemannian Geometry, and Topology. What else is needed?