2014 Reprint of 1955 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Reprint of the 3rd Edition. Weyl was a German American mathematician who, through his widely varied contributions in mathematics, served as a link between pure mathematics and theoretical physics, in particular adding enormously to quantum mechanics and the theory of relativity. Hermann Weyl (1885-1955) was perhaps the most important and, above all, the most multifaceted of David Hilbert’s students. His life’s work encompassed such varied disciplines as number theory, complex analysis, mathematical physics, and geometry. His youthful work The Concept of a Riemann Surface, which was published in 1913 by Teubner, in Leipzig, quickly achieved acclaim as an epochal work, a work that exerted lasting influence on several branches of mathematics.