The book includes the geometry of Euclid and Minkowski spaces, their transformation groups, classical geometry of curves and surfaces, tensor analysis and Riemannian geometry, variational calculus and field theory, and the foundations of relativity theory. geometry and topology of manifolds, including the foundations of homotopy and stratification theory, some of their applications, in particular, to gauge field theory. The book is designed for students - mathematicians, mechanics, theoretical physicists, starting from the 2nd year of the university, and provides courses in geometry, read for 2-3 years of study. More complex sections of the book will also be useful for senior students, graduate students and researchers .