The work “Analytical and topological methods of investigations of equations with partial derivatives, problem of complex and hypercomplex analysis” is dedicated to solving some important problems of Complex Analysis, Theory of monogenic functions in commutative Banach algebras and Convex Analysis. The main results are described in 25 leading papers. Among them there are: finding integral expressions of generalized axial-symmetric potentials via analytic functions of complex variable; development of methods of solving boundary value problems for generalized axial-symmetric potentials via analytic functions of complex variable; characterization of generalized axial-symmetric potentials by means of monogenic functions taking values in infinite commutative Banach algebra, and constructive description and finding analytic properties of monogenic functions taking values in commutative Banach algebra, solving of the algebraic quaternion equations and their systems; finding of criteria of the convexity of sets in multi-dimensional spaces; finding a measure witch is an invariant with respect to complex linear unimodular transformations and constructing of corresponding integral formula.