The textbook is written on the basis of the experience of teaching the authors at the Moscow State University . M. In. Lomonosov . Throughout the book there is a parallel consideration of the cases of plane and space. The vector algebra. is described in great detail. When it is presented, the concept of linear dependence of vectors is immediately introduced, and on its basis the possibility of unambiguous decomposition of the vector on an affine basis . is established. Issues of second-order image theory (optical properties, polar equations, etc.) are not ignored. p. ). The appendix to the book contains material that is not included in the traditional courses of analytical geometry. For students of physical and physico-mathematical faculties and faculties of computational mathematics and cybernetics of universities .