The book is based on a course of lectures that have been given to students of the Faculty of Mechanics and Mathematics of Moscow State University since 2012. M.V. Lomonosov. This course of lectures is new, it deals with deep and important issues that at the same time allow for visual presentation and informal discussion. While maintaining a high level of rigor, the authors also tried not to miss the opportunity to show the beauty and clarity of the geometric ideas and structures discussed.