We obtained new results in complex analysis in the area of several complex variables, in particular in the following subareas: (A) holomorphic embeddings and proper holomorphic maps (B) characterizations of Cauchy-Riemann functions on boundaries in terms of their restrictions to lower dimensional manifolds (C) holomorphic automorphisms of C^n and Fatou-Bieberbach maps (D) analytic sets with boundaries in totally real submanifolds (E) homotopy principle of Gromov The main results are the following: (A) We proved the existence of proper holomorphic discs in Stein manifolds passing through a discrete set, we obtained a new proof of holomorphic embeddability of planar domains into C^2 and proved theorems about holomorphic embeddability of Stein manifolds of dimension at least 2 into euclidean spaces of minimal dimension with additional interpolation on discrete sets. We obtained new results about holomorphic embeddability of finite Riemann surfaces into C^2. We also proved that injective proper maps from the disc into C^2 admit interpolation with holomorphic embeddings and proved the existence of proper holomorphic images of discs in C^2 that miss both coordinate axes. (B) We proved a new Morera theorem for functions on the sphere of C^2 with conditions along the intersections of the sphere with real hyperplanes. We obtained new results about holomorphicity of rational functions of two real variables which admit holomorphic extensions from families of circles, and general results about holomorphicity of continuous functions that admit holomorphic extensions from open familes of circles. (C) We obtained new results about approximation of diffeomorphisms between totally real submanifolds of C^n with biholomorphic maps in tubular neighbourhoods .and with holomorphic automorphisms of C^n. (D) We proved that given an selection above the sphere in C^n with fibers which are totally circular domains in C^n, its polynomial hull can be exhausted by analytic discs. We proved the existence of generalized Ahlfors functions on finite Riemann surfaces with genus g and with m boundary components, which have 2g+m-1 zeros. (E) We obtained new results about global extensions of sections of holomorphic submersions above Stein spaces which admit stratified sprays. We constructed complex submanifolds of C^5 which are smooth complete intersections but not holomorphic complete intersections. We proved that the Gromov h-principle holds for holomorphic maps from Stein manifolds into subelliptic complex manifolds. We proved a version of h-principle for multiple valued sections of branched holomorphic maps to Stein manifolds. We proved the existence of regular Stein neighbourhoods of closed real surfaces in complex surfaces. We proved the existence of noncritical holomorphic functions an any Stein manifold which solved a problem open for 40 years. We collaborated with people from several mathematical centers (University of Wisconsin, Madison, University of Michigan, University of Washington, Indiana University in the USA, Universite Paul Sabatier, Toulouse in France, University of Oslo, Norway, Bar-Ilan University, Israel). Our results were published in 33 articles in high quality mathematical journals . We had 19 invited lectures on international conferences, 34 invited lectures at various universities. Beside this, we had a series of 14 lectures at a university abroad and a series of lectures at an international summer school.