The textbook corresponds to the MIPT program and contains the theory of limits, differential and integral calculus of functions of one and several variables, numerical and functional series, trigonometric Fourier series, Fourier transforms, elements of normalized and Hilbert spaces and other topics. It was written on the basis of lectures given for many years at the Moscow Institute of Physics and Technology by the author (professor at the Moscow Institute of Physics and Technology, Corresponding Member of the Russian Academy of Sciences, head of the Department of Function Theory of the Steklov Mathematical Institute of the Russian Academy of Sciences). Designed for students of physical and mathematical and engineering physics specialties of universities with increased training in mathematics.