The book is intended for everyone who, having knowledge of the basics of the school course of mathematics, wants to systematize their knowledge, and also seeks to successfully pass the exam and entrance exams to the university. The manual will be useful for students of pedagogical universities, as well as teachers of secondary schools. Each section of the manual contains the necessary reference material and detailed examples taken from the MIPT Olympiads and the practice of entrance exams to universities, which impose rather high requirements on the mathematical training of applicants. In addition, the manual includes tasks for independent work of students. All tasks are answered, and some of the most difficult ones are given brief instructions.