The book considers traditional sections of the school course of algebra at a higher level compared to the basic level and sections that are not included in the circle of tasks of the basic level necessary for passing the exam in mathematics of the profile level: arithmetic and algebraic transformations, graph transformations, indicative and logarithmic equations and inequalities, combinatorics and elements of probability theory. An analysis of the text tasks on these topics is given in the corresponding chapters. Each chapter briefly presents the necessary theoretical information, a large number of problems with comments and solutions, approaches and methods for solving classes of problems, problems for independent solution. Answers are given at the end of the manual.