• 1. Scalar curvature and geometrization conjectures for 3-manifolds Michael T. Anderson; 2. Injectivity radius estimates and sphere theorems Uwe Abresch and Wolfgang T. Meyer; 3. Aspects of Ricci curvature Tobias H. Colding; 4. A genealogy of noncompact manifolds of nonnegative curvature: history and logic R. E. Greene; 5. Differential geometric aspects of Alexandrov spaces Yukio Otsu; 6. Convergence theorems in Riemannian geometry Peter Petersen; 7. The comparison geometry of Ricci curvature Shunhui Zhu; 8. Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers G. Perelman; 9. Collapsing with no proper extremal subsets G. Perelman; 10. Example of a complete Riemannian manifold of positive Ricci curvature with Euclidean volume growth and with nonunique asymptotic cone G. Perelman; 11. Applications of quasigeodesics and gradient curves Anton Petrunin.

Review of the hardback: '… a beautiful, comprehensive and up-to-date collection of expository experts in the field.' European Mathematical Society