The book is intended for everyone who, having knowledge of the basics of the school mathematics course, wants to systematize their knowledge, and also strives to successfully pass the exam and university entrance exams. 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 fairly high requirements on the mathematical training of applicants. In addition, the manual includes tasks for independent work of students. All problems are answered, and some of the more difficult ones are given short instructions.