The collection is made in accordance with the program in mathematics for students in higher education. It consists of two parts: "Arithmetic, algebra, geometry" (part I); "Algebra, geometry (additional tasks). The beginning of the analysis. Coordinates and vectors" (part II). All tasks of part I are divided into three groups by level of difficulty. Each Chapter provides information and reference material and examples of solving problems. For all tasks answered. The manual is addressed to students, graduates and teachers of mathematics.