The book sets out the fundamentals of mathematical analysis approximately in the sequence in which they were created and improved by the great mathematicians of the past. The first two chapters show how calculations involved in solving practical problems led to the discovery of infinite series, differential and integral calculus, and differential equations. Chapters III and IV are devoted to the formation of a mathematically rigorous theory in these areas of analysis of functions of one and several variables in the 19th century. The book contains a large number of examples, calculations and illustrations, which allows us to better understand the motivating reasons for many mathematical discoveries and give them deep explanations.< /p>