About the Book

The English edition has been thoroughly revised in line with comments and suggestions, made by our readers, the mistakes and misprints that were detected have been corrected. This is essentially a textbook for modern course on differential geometry and topology, which is much wider than the traditional courses on classical differential geometry, and it covers many branches of mathematics a knowledge of which has become essential for a modern mathematical education. We hope that a reader who has mastered this material will be able to do independent research both in geometry and related fields. To gain a deeper understanding of the material of this book, we recommend the reader should solve the questions in A. S. Mishchenko, Yu. P. Solovyev and A. T. Fomenko Problems in Differential Geometry and Topology which was specially compiled to accompany this course.