"An elegant piece of work, suitable as a text for the beginning student as well as pleasant and informative reading for the mature mathematician." -- Scripta Mathematica This critically acclaimed text by a major twentieth-century mathematician presents a detailed theory of Fréchet (V) spaces and a comprehensive examination of their relevance to topological spaces, plus in-depth discussions of metric and complete spaces. The author's exposition is clear and refined. Moreover, his axiomatic treatment of the theory of point sets, apart from its logical simplicity, has also an advantage: it supplies excellent material for exercise in abstract thinking and logical argument in the deduction of theorems from stated suppositions alone -- that is, in proving theorems by drawing on strictly logical conclusions, without appeal to intuition. Numerous worked and unworked examples supplement each chapter.