The foundations of functional analysis and operator theory are set forth: the theory of measure and integral, normalized spaces and functionals and operators in them, the spectral theory of self-adjoint operators in Hilbert spaces (including unlimited operators and the theory of decompositions by generalized eigenvectors), elements of the theory of generalized functions of both finite and infinite order, the theory of integral equations. The theoretical material is illustrated by a large number of examples and exercises for independent work. The presentation is carried out taking into account possible applications to the problems of modern mathematical physics. For university students studying in the specialty "Mathematics." It can be used by students of technical schools and pedagogical institutes, graduate students and researchers.