The monograph deals with the main sections of the theory limits, differential and integral calculus functions of one and several variables and their application. Contains a large number of illustrative exercises and tasks, as well as solved tasks - standards for independent work of students. For students and teachers of physical and mathematical specialities.The manual contains 4 sections covering the fundamental topics of mathematical analysis: definition sets of real numbers, limit of a numerical sequence, functions of one and several variables, differential calculus of functions of one and several variables. The material is arranged and distributed in such a way that the reader, whether a teacher or a student, can easily prepare a summary for independent work. Traditional deductive (with evidence) style presentation of fundamental theoretical sections is aimed at creating a solid logical base and the necessary knowledge and skills.