The major part of this two-volume textbook stems from the course in mathematical analysis given by the author for many years at the Moscow Physico-technical Institute.The first volume consisting of eleven chapters includes an introduction (Chapter 1) which treats of fundamental notions of mathematical analysis using an intuitive concept of a limit. With the aid of visual interpretation and some considerations of a physical character it establishes the relationship between the derivative and the integral and gives some elements of differen­ tiation and integration techniques necessary to those readers who are simultaneously studying physics.The notion of a real number is interpreted in the first volume (Chapter 2) on the basis ofits representation as an infinite deci­mal.Chapters 3-11 contain the following topics: Limit of Se­quence, Limit of Function, Functions of One Variable, Func­ tions of Several Variables, Indefinite Integral, Definite Integral, Some Applications of Integrals, Series.