The book contains theoretical material and tasks for the course of elementary mathematics . The theoretical material includes a presentation of the most difficult questions of the school course of algebra and elementary functions. Particular attention is paid to those sections of the course that are not fully covered in the educational literature . A significant part of the tasks contained in the book were offered at the entrance exams at MIPT . Many tasks are specially compiled by the authors for this book. The book is intended for teachers of mathematics, students of pedagogical universities, universities and especially for high school students preparing for universities .