The textbook corresponds to the program of courses Functional analysis, Operator theory, Analysis III, which are read in universities and pedagogical universities. The book presents the main theoretical-multiple concepts, the general theory of metric, topological, linear topological and normed spaces, the general theory of measure, measurable functions and the Lebesgue integral. The theory of operators in Hilbert space, the spectral theory of self-adjoint operators, the application of the methods of the theory of analytical functions in the spectral theory of non-self-adjoint operators, the Fourier transform theory and generalized functions. are considered in detail. For students of universities and pedagogical universities . Can be useful for university students with advanced study in mathematics, graduate students and researchers.