Table of Contents

Background from Riemannian geometry and Ricci flow: Preliminaries from Riemannian geometry Manifolds of non-negative curvature Basics of Ricci flow The maximum principle Convergence results for Ricci flow Perelman's length function and its applications: A comparison geometry approach to the Ricci flow Complete Ricci flows of bounded curvature Non-collapsed results $kappa$-non-collapsed ancient solutions Bounded curvature at bounded distance Geometric limits of generalized Ricci flows The standard solution Ricci flow with surgery: Surgery on a $delta$-neck Ricci flow with surgery: The definition Controlled Ricci flows with surgery Proof of non-collapsing Completion of the proof of Theorem 15.9 Completion of the proof of the Poincare conjecture: Finite-time extinction Completion of the proof of Proposition 18.24 3-manifolds covered by canonical neighborhoods Bibliography Index.