Topping P. Lectures on the Ricci Flow

Cambridge: Cambridge University Press, 2006. — 122 p.An introduction to Ricci flow suitable for graduate students and research mathematicians.Preface
Introduction
Riemannian geometry background
The maximum principle
Comments on existence theory for parabolic PDE
Existence theory for the Ricci flow
Ricci flow as a gradient flow
Compactness of Riemannian manifolds and flows
Perelman’s W entropy functional
Curvature pinching and preserved curvature properties under Ricci flow
Three-manifolds with positive Ricci curvature, and beyond
Appendix A. Connected sum
References
Index