‎WEYL, HERMANN.‎
‎Die Idee der Riemannschen Fläche. (Mathematische Vorlesungen an der Universitat Göttingen, no. V).‎

‎Leipzig und Berlin, B.G. Teubner, 1913. Orig. green printed wrappers. Frontwrapper nearly loose but without loss. Backstrip faded. Very small nicks to spineends. IX,(1),169,(1) pp. + Publishers catalogue. Textillustrations. Internally clean and fine.‎

Reference : 38939

‎Scarce first edition. As privatdozent Hermann Weyl had given a course on Riemann's theory of functions" but instead of following his predecessors in their constant appeal to intuition for the definition and properties of Riemann surfaces, he set out to give to their theory the same kind of axiomatic and rigorous treatment that Hilbert had given to Euclidean geometry. Using Hilbert's idea of defining neighborhoods by a system of axioms, and influenced by Brouwer's clever application of Poincare's simplicial methods (which had just been published), he gave the first rigorous definition of a complex manifold of dimension 1 and a throughout treatment (without any appeal to intuition) of all the questions regarding orientation, homology, and fundamental groups of these manifolds. ""Die Idee der Riemannschen Fläche"" (1913) immediately became a classic and inspired all later developments of the theory of differential and complex manifolds.(J.Dieudonne in DSB).‎