This transcript transforms mathematics from geometrization to materialization of space. It is classic evolution of complex algebra A. Cauchy into space. It gives mathematical foundation to the core physic theories; gives them a completely new interpretation in complex space. Table of contents: Problems of contemporary mathematics. Extension of complex variable of A.L. Cauchy into space. Functions of complex spatial variable. Functions differentiability. Implementation of integral theorems of A.L. Cauchy in space. Connectivity of complex space. Implementation of integral theorems in space. Calculation of curvilinear integrals in complex space. Extension of Integral theorems for multi-connected regions in complex space. Integral theorems of A.L. Cauchy in space. Numeric series in space. Abel's theorem. Taylor series. Laurent series. Isolated special points in space. Residue in complex space. Taking integrals in space with residues. Representing of primary relativity theory equations. New mathematical system means new calculation methods in theoretical physics. Lorentz transformation. Energy in space. Self-coordination of interacting spaces. Time relativity. Michelson-Morley experiment. Implementation of methods of "theory of functions of complex spatial variable" in theoretical physics. Calculation of quantum transformations in hydrogen. Ether. Complex spatial variable field in Special Relativity Theory. New concept of space. Binding energy of atomic nucleus. Electromagnetic and numeric field of complex space.