The textbook for students of physical and mechanical-mathematical specialties of universities is written on the basis of a course of lectures given by the author at the Moscow Institute of Physics and Technology. In fact, it is accepted as a textbook in some universities with an increased mathematics program. The book contains the differential and integral calculus of functions of one and many variables, field theory, Fourier series and integrals, the beginnings of Banach space theory, and generalized functions.