This text for second-year graduate students provides an introduction to differential geometry, with an emphasis on Riemannian geometry. The main theorems are presented in complete detail, but the student is expected to provide the details of certain arguments. The five chapters cover definitions and the theorems of Whitney and Sard, vector fields and differential forms, integration of vector fields and p -plane fields, connections, Riemannian manifolds, some problems in partial differential equations, and global notation. Annotation c. Book News, Inc., Portland, OR (booknews.com)