High dimensional convex bodies: phenomena, intuitions and results

Phenomena in large dimensions appear in a number of fields of mathematics and related fields of science, dealing with functions of infinitely growing number of variables and with objects that are determined by infinitely growing number of parameters. In this talk we trace these phenomena in linear-metric, geometric and some combinatorial structure of high-dimensional convex bodies. We shall concentrate this presentation on very recent results in Asymptotic Geometric Analysis.