The book belongs to the pen of a prominent American mathematician, known not only for numerous scientific studies, but also for beautifully written textbooks. Many of his articles and books have been translated into Russian. W. Rudin's textbook is distinguished by a thoughtful selection of material, a masterful presentation, and an analysis of non-trivial examples of applications of functional analysis in other areas of mathematics. The book has three main parts: general theory; Fourier distributions and transformations; Banach algebras and spectral theory.