Conference held June 2127, 1990 at the University of Massachusetts, Amherst.

Includes bibliographical references.

Theta vanishings for some smooth abelian coverings of Riemann surfaces ; The period matrix of Macbeath's curve of genus seven ; The continued fraction parameter in the deformation theory of classical Schottky groups ; The fibers of the Prym map ; Some Riemann surfaces whose Jacobians have strange product structures ; The Schottky relation in genus ; The trisecant formula and hyperelliptic surfaces ; The nonabelian Szego kernel and thetadivisor ; Theta functions on the boundary of moduli space ; Geometry of the Fano threefold of degree 0 of the first type ; Some uses of analytic torsion in the study of Weierstrass points ; A problem of Narasimhan ; On the reduction of Abelian integrals and a problem of H. Hopf ; Normalization of the Krichever data ; Splittable Jacobi varieties ; Theta divisors for vector bundles Robert D M Accola ; Kevin Berry and Marvin Tretkoff ; Robert Brooks ; Ron Donagi ; Clifford J Earle ; Leon Ehrenpreis ; Hershel M Farkas ; John Fay ; Gabino Gonzalez Diez ; Atanas Iliev Iliev ; Jay Jorgenson ; George R Kempf ; Henrik H Martens ; Motohico Mulase ; John F X Ries ; Montserrat Teixidor i Bigas and Loring W Tu