The book offered to the attention of the reader was written by a team of employees of the Faculty of Mechanics and Mathematics of Moscow State University . M. In. Lomonosov . It is a complete and systematic course designed for intensive mathematical preparation for admission to any university. The manual is written on the basis of many years of experience of the authors with the most diverse levels of training for students and entrants. All authors have repeatedly been managers or members of examination boards in mathematics at various faculties of Moscow State University and in other universities, which allowed them to warn the reader from numerous typical mistakes that are allowed by entrants to exams .. So that the applicant could avoid such errors, the manual used the most simple methods of teaching problem solving, which helped many generations of applicants to successfully pass the entrance exams in mathematics in a variety of universities.