Comparison Geometry asks: What can we say about a Riemannian manifold if we know a (lower or upper) bound for its curvature, and perhaps something about its topology?

This volume, arising from a 1994 MSRI program, is an up-to-date panorama of Comparison Geometry, featuring surveys and new research. Surveys present classical and recent results, and often include complete proofs, in some cases involving a new and unified approach. The historical evolution of the subject is summarized in charts and tables of examples. This volume will be a valuable source for researchers and graduate students in Riemannian Geometry.