Reference manual includes the following sections: introduction to analysis, differential and integral calculus of functions of one variable, differential calculus of functions of several variables, differential equations, numerical methods. The manual contains definitions of basic concepts, corresponding formulas, more than 400 basic, key examples with detailed solutions. At the end of each paragraph are tasks for self-solution, answers are given, instructions are given for some tasks. Will help in preparation for practical classes, tests and exams, and students of correspondence departments - independently perform test work. Intended for students and university teachers.