The textbook was written in accordance with the program of the course "Mathematical Analysis" for technical schools in the specialty "Applied Mathematics." It is distinguished by a high scientific and methodological level of presentation of the material. In addition to mathematical analysis, the textbook includes sections such as elements of mathematical logic, theory of functions of a complex variable. The presentation is illustrated by a large number of examples. Complex evidence is divided into clear semantic stages, there are a number of educational algorithms that provide an indicative basis for actions to solve a particular range of problems.