Peter Topping is a Senior Lecturer in Mathematics at the University of Warwick.

"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical Reviews

• 1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.

Peter Topping is a Senior Lecturer in Mathematics at the University of Warwick.

"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical Reviews

• 1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.

Peter Topping is a Senior Lecturer in Mathematics at the University of Warwick.

"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical Reviews

• 1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.