This volume presents twelve outstanding papers which have had a deep influence upon the development of geometry during the last fifty years. Among the authors and topics are: H. P. McKean, Jr. and I. M. Singer on curvature and the eigenvalues of the Laplacian; Eugenio Calabi on minimal immersions of surfaces in Euclidean spheres; H. Blaine Lawson, Jr. and Shing-Tung Yau on compact manifolds of nonpositive curvature; Mikhael Gromov on filling Riemannian manifolds; G. Perelman on a proof of the soul conjecture of Cheeger and Gromoll; and Jeff Cheeger and Tobias H. Colding on the structure of spaces with Ricci curvature bounded below. With a preface by Shing-Tung Yau.