The name of Paul Halmos is very popular in the mathematical world and is well known to the Soviet reader, who highly appreciated his books "Theory of Measure," "Lectures on Ergodic Theory" and "Finite-Dimensional Vector Spaces." His new book is an original textbook on the theory of Hilbert spaces and their applications, designed for an active reader. The book is undoubtedly useful to a wide range of readers, especially students and teachers of functional analysis, as well as all those who want to refresh and replenish their knowledge in one of the most important sections of modern mathematics - the theory of Hilbert spaces. Theoretical physicists will also be interested in her.