  After Weyl’s (1910b) habilitation, he became a Privatdozent and was  thereby entitled to give lectures at the University of  Göttingen. Weyl chose to lecture on Riemann’s theory of  algebraic functions during the winter semester of 1911–12.  These lectures became the basis of Weyl’s (1913) first book Die  Idee der Riemannschen Fläche (The Concept of a Riemann  Surface). This work, in which function theory, geometry and  topology are unified, constitutes the first modern and comprehensive  treatment of Riemann surfaces. The work also contains the first  construction of an abstract manifold. Emphasizing that the `points of the manifold’ can be quite arbitrary, Weyl based his definition of a  general two-dimensional manifold or surface on an extension of the  neighbourhood axioms that Hilbert (1902) had proposed for the  definition of a plane. The work is indicative of Weyl’s exceptional  gift for harmoniously uniting into a coherent whole a patchwork of  distinct mathematical fields.