Matrix domains in the theory functions of several complex variables

The theory functions of several complex variables or multidimensional complex analysis, despite the various approaches presented in the exposition, currently has a fairly strictly constructed theory. At the same time, many issues of classical (one-dimensional) complex analysis still do not have unambiguous multidimensional analogues. This is due to the complex structure of the multidimensional complex space, the polysemy (overdetermination) of the Cauchy - Riemann conditions, the absence of a universal Cauchy integral formula, etc. In the works of E.Kartan, K.Siegel, Hua Lo-Ken, I.I.Pyatetskiy-Shapiro, B.V.Shabat widely used matrix approach presentation of the theory of multidimensional complex analysis ([1-4]). Here, classical fields and the related problems of the theory of functions and geometry are mainly investigated. The importance of studying classical domains is that they are not reducible, i.e. these areas are in some sense model areas of multidimensional space. The report presents the latest results in multidimensional complex analysis related to classical domains.