These lectures were delivered by the author in 1972 at the Faculty of Mechanics and Mathematics of Moscow State University for teachers of universities of the country, students of the Faculty of Advanced Studies . In the lectures, we sought, on the one hand, to present the fundamental material of classical functional analysis - the theory of spaces and operators, and, on the other hand, to show how the methods and ideas of the theory of analytical functions allow us to take a fresh look at the traditional problems of analysis ........ For example, on the problem of whether the system of eigenfunctions of the operator is complete in space, the basis of space, and t. d. I want to say a few words about the tasks..... [ There are many of them in the text: after each paragraph 10 tasks. They tend to be of varying complexity - from simple exercises to meaningful theorems. There are also problems whose solutions are unknown to the author .. When reading a book, you should try to solve problems, some of the statements contained in them are used in the future. Compared to what was read in the lectures, this edition produced minor changes of a methodical nature, and also included the work of M. In. Keldysh "On the completeness of the proper functions of certain classes of non-self-adjoint linear operators". The author expresses deep gratitude to his students, students of Bashkir State University N. Asadullina and N. Mironenko for assistance in the design of the manuscript .