Moscow: Independent university of Moscow, 2011. — 160 p.
This brochure is an expanded version of the lectures on the course "Geometries" given by the author in the fall of 2003 at the Independent University of Moscow (IUM). The book is written in english, which, according to the author's idea, will help future mathematicians to join the international mathematical culture. Each lecture is provided with problems, the solution of which contributes to a better assimilation of the material. Сhapter means lecture.