The book provides an elementary introduction to modern theory of topological vector spaces. Although its volume is small, it contains a fairly complete summary of the most important concepts and results of this theory, connecting the high scientific level with the highest possible availability. The authors focus on the study of locally convex spaces and present the most significant results and ideas related to this important class of spaces. Information of General topology are introduced during the presentation as needed.

The book can be used for initial introduction to the theory of topological vector spaces; it is available to graduate students n students of senior courses of universities and pedagogical Institute. At the same time, it is of interest n for professional mathematicians interested in functional analysis and topology.