The textbook contains a lecture summary on the mandatory course of analytical geometry, read by the authors for a number of years for first-year students of the Faculty of Mechanics and Mathematics of Moscow State University. The main feature of this course, first read by the first author and then revised by the second, is the focus of the theory of conic sections, which allowed, along with conventional analytical constructions, to more clearly represent the geometric side of the subject. For first-year students.