Asymptotic Geometric Analysis is mainly concerned with geometric and linear properties of finite dimensional objects, such as convex sets and normed spaces, especially with the characteristic behavior that emerges when the dimension, or a number of other relevant free parameters, is suitably large or tends to infinity. High-dimensional systems are very frequent in mathematics and applied sciences hence understanding of high-dimensional phenomena is becoming increasingly important. The last decade has seen a tremendous growth of Asymptotic Geometric Analysis, with the development of new powerful techniques, mainly of probabilistic flavor. By virtue of Asymptotic Geometric Analysis general framework, methods, and its impact on related fields, Asymptotic Geometric Analysis can be situated at the "crossroads" of many branches of mathematics: functional analysis, convex and discrete geometry, several areas of probability, among others. In particular, many phenomena are closely related to the behavior of singular values of random matrices as well as to the problem of approximating of the covariance matrix by the random sampling.