"Functional analysis is the study of certain topological-algebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems. A good introductory text on this subject should include a presentation of its axiomatics (i.e., of the general theory of topological vector spaces), it should treat at least a few topics in some depth, and it should contain some interesting applications to other branches of mathematics. A fairly large part of the general theory is presented without the assumption of local convexity. The basic properties of compact operators are derived from the duality theory in Banach spaces. The Krein-Milman theorem on the existence of extreme points is used in several ways in chapter 5. The theory of distributions and Fourier transforms is worked out i fair detail and is applied. As well as; Wiener's tauberian theorem; Gelfand-Naimark characterization; Banach algebras; Lebesgue integration; properties of holomorphic function; Cauchy's theorem; Runge's theorem".