The manual contains an exposition of the foundations of the general theory of measure and integral, as well as classical special cases - Lebesgue and Lebesgue-Stieltjes measures and integrals. The book includes: a description of the basic classes of sets and properties of measures, continuation theory, charge properties, the theory of measurable maps and functions, Lebesgue integral theory, in particular the properties of parameter-dependent Lebesgue integrals, the general variable replacement formula, the Radon-Nicodemus theorem, and the Fubini theorem. The main properties of functional spaces are given. Theoretical material is accompanied by exercises for independent work.