Table of Contents

Riemannian geometry Fundamentals of the Ricci flow equation Closed 3-manifolds with positive Ricci curvature Ricci solitons and special solutions Isoperimetric estimates and no local collapsing Preparation for singularity analysis High-dimensional and noncompact Ricci flow Singularity analysis Ancient solutions Differential Harnack estimates Space-time geometry Appendix A. Geometric analysis related to Ricci flow Appendix B. Analytic techniques for geometric flows Appendix S. Solutions to selected exercises Bibliography Index.