The Concept of a Riemann Surface. Translated. by Gerald R. Maclane. Third Edition, 1955.

First Edition in English of Die Idee der Riemannschen Fläche (1st ed., 1913; 2d ed., 1923), from the 1955 Third (final) Edition. x, 1 leaf, 191 pp. Original cloth. Near Fine, without dust jacket. See Preface (pp. vii-x) for significant changes to this edition. 'Another early work [Weyl was 28 when he published it] was his now famous book on Riemann surfaces (1913). Here we see Weyl at his majestic best, imposing coherence, elegance, and order on a classical subject and thereby laying proper foundations for its future development. Already with the work of Riemann it was clear that the classical theory of functions of a complex variable could not be confined to the complex plane: branched coverings of the plane were necessary, but it was Weyl who put this into its proper form, getting away from the complex plane by introducing the notion of an abstract surface. Coming when it did in 1913 it was the right book at the right time, providing the model for all subsequent work on higher-dimensional manifolds. With its emphasis on vector spaces (which Weyl was the first to define) it provided the right language for both geometry and algebra. It also prepared the way for the topologists who followed' (Michael Atiyah, Biographical Memoirs, National Academy of Sciences; please ask for on-line source). 'The outstanding characteristic of Weyl's work was his ability to unite previously unrelated subjects. In Die Idee der Riemannschen Fläche (1913; The Concept of a Riemann Surface, 1964) he created a new branch of mathematics by uniting function theory and geometry, thereby opening up the modern synoptic view of analysis, geometry, and topology' (please ask for on-line source).…