The book is one of the best and historically one of the first popular works in mathematics written by major mathematicians. The book contains, indeed, a very visual, but rather strict story about geometric sciences and theories, in particular about geometric crystallography, about the geometric essence of kinematics and about topology. The book is quite accessible to high school students interested in mathematics. At the same time, in many chapters it complements well, without duplicating, the course of university mathematics. This book will be read with pleasure by a mature mathematician who accidentally did not get acquainted with it in the process of his mathematical education.