Riemannian Geometry

The author's intent behind this book was to provide to advanced undergraduate and graduate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications. A special feature of the book is an appendix, which has been considerably revised and expanded as compared to the original Japanese edition, on the collapsing of Riemannian manifolds and Gromov's convergence theorem. With special emphasis placed on understandability and readability and with many problems included, the book is suitable as a text for a course in differential geometry for well-prepared and motivated graduate students. It can also serve as a good reference for a practicing mathematician interested in Riemannian geometry.