ISBN10: 0817626506, ISBN13: 9780817626501, [publisher: Basel, etc.: Birkhäuser, 1992.] Hardcover First Edition First Edition in English. Frontispiece, 197 pp; illus. Original decorated matte boards. Near Fine, without dust jacket (as issued). 'Beginning in the 1940s, Weil started the rapid advance of algebraic geometry and number theory by laying the foundations for abstract algebraic geometry and the modern theory of abelian varieties. His work on algebraic curves has influenced a wide variety of areas, including some outside mathematics, such as elementary particle physics and string theory. In fact Weil's work in this area was basic to work by mathematicians such as [Shing-Tung] Yau who was awarded a Fields Medal in 1982 for work in three dimensional algebraic geometry which has major applications to quantum field theory. Yau is not the only mathematician who received a Fields Medal for work which continued that begun by Weil. In 1978 Deligne was awarded a Fields Medal for solving the Weil Conjectures. Again we quote [4] for a description of Weil's fundamental contribution: 'One of Weil's major achievements was his proof of the Riemann hypothesis for the congruence zeta functions of algebraic function fields. In 1949 he raised certain conjectures about the congruence zeta function of algebraic varieties over finite fields. These Weil conjectures, as they came to be called, grew out of his deep insight into the topology of algebraic ...