About the book This problem book is compiled by eminent Moscow university teachers.Based on many years of teaching experience at the mechanics-and-mathematics department, it contains problems practically for all sections of the differential geometry and topology course delivered for university students: besides classical branches of the theory of curves and surfaces, the reader win be offered problems in smooth manifold theory, Riemannian geometry, vector fields and differential forms,general topology, homotopy theory and elements of variational calculus. The structure of the volume corresponds to A Course of Differential Geometry and Topology (Moscow University Press 1980)  by Prof. A. T. Fomenko and Prof. A. S. Mishchenko Some problems however, touch upon topics outside the course lectures. The corresponding sections are provided with all necessary theoretical foundations.Preface 51. Application of Linear Algebra to Geometry 72. Systems of Coordinates 93. Riemannian Metric 144. Theory of Curves 165. Surfaces 346. Manifolds 537. Transformation Groups 608. Vector Fields 649. Tensor Analysis 7010. Differential Forms, Integral Formulae, De RhamCohomology 7511. General Topology 8112. Homotopy Theory 8713. Covering Maps, Fibre Spaces, Riemann Surfaces 9714. Degree of Mapping 10515. Simplest Variational Problems 108Answers and Hints 113Bibliography 208