This issue of the SMB series contains large material, mainly grouped around the theory of operators and operator equations. Here are presented the basic concepts and methods of functional analysis, the theory of operators in Hilbert space and in spaces with a cone, the theory of nonlinear operator equations, the theory of normalized rings, applications to equations in partial derivatives, to integral equations .. A separate chapter is devoted to the main operators of quantum mechanics A significant place in the book is occupied by the presentation of the theory of generalized functions, provided with a number of tables. The nature of the presentation here is descriptive; mathematical facts are explained in a logically coherent form; theorems and formulas are usually given without proof. The main attention is paid to the ideological side of the issue, not obscured by unnecessary details .. The book is intended for mathematicians, mechanics and physicists. It will find a lot of useful for themselves students and graduate students of relevant specialties .