The general theory of topological vector spaces was founded during the period which goes from 1920 to 1930 approximately. But it had been prepared for a long time before by the study of numerous problems of Functional Analysis; and its history cannot be retraced without indicating, at least summarily, how the study of these problems gradually brought mathematicians (especially from the beginning of the XXth century) to become aware of the common ancestry of the questions under consideration, and of the possibility of formulating them in a much more general way and of applying to them uniform solution procedures.