Vectors, tensors, spinors, twistor, genus: Searching for the primary geometric element

What geometric objects underlie the universe? What newly brought up for the past half -century mathematics and physics in ordinary ideas about geometry stated in school and institute textbooks? This small book gives the first ideas about mathematical constructions, both long -used physicists (vectors, tensors, spinors), and recently arose in the bowels of modern attempts to agree on a purely geometric approach to the general theory of relativity and algebraic in essence the approach of quantum mechanics.
A brief (if necessary) historical overview of the development of the concept of number and difficult ways to introduce vector and tensor methods into the practice of readers. Acquaintance with new geometric ideas proposed by modern competing physical theories (strings theory, loop gravity, super -symmetry) will be useful not only to future physicists, but also by a wider audience. The aim of this work is to convey to this audience a new paradigm about the basic elements that form the geometry of our world, and about attempts to go beyond its limits