The manual corresponds to the first part of the lecture course of the first semester in mathematics and is intended for undergraduate students of economic areas of full-time and part-time education. It can be used when studying a mathematics course by bachelors of certain technical areas with a small amount of mathematics. The issues of linear algebra and analytic geometry are considered. The manual includes a large number of problems illustrating the topics studied, as well as examples of problems of economic content, the solution of which is based on the studied sections of mathematics.