Basics of mathematical analysis: function of several variables, differential equations, multiple integrals : Training manual for students studying under the bachelor program in the areas of training 141100 - Energy engineering, 140400 - Electric power engineering and electrical engineering, 140100 - Thermal power engineering and thermal engineering, 141403 - Nuclear power plants : design, operation and engineering, 280700 - Technospherical safety . The textbook consists of three chapters: functions of several variables, differential equations, multiple integrals. The first chapter introduces the concepts of the function of several variables, the limit of a given function at a point, the continuity and differentiability of a function. The extremity of the function of several variables is considered. The second chapter is devoted to the main types of differential equations of the 1st order, equations of the nth order, allowing a decrease in the degree, as well as linear equations of the nth order .. In the third chapter, the concepts of double and triple integral are introduced and methods of their calculation in various coordinate systems are given. All of the above topics are illustrated with examples. The textbook is intended for students of all specialties and all forms of education studying the course "Mathematics" .