Theta functions have a long and distinguished history and play a many-faceted and central role in a number of areas of mathematics. Interest in these functions has rekindled in recent years as a result of the wide variety of areas in which they have made major contributions. Crossing the lines of semi-simple Lie group theory and nilpotent Lie group theory, theta functions are relevant to the arithmetic of quadratic forms and to partition theory, through which they relate to statistical mechanics and quantum field theory. In addition, they are used to study Riemann surfaces, abelian varieties, and solutions of differential equations from physics. In this way, they relate to partial differential equations and algebraic geometry.

This two-volume collection contains the proceedings of an AMS Summer Research Institute on Theta Functions, held in July 1987 at Bowdoin College. With papers by some of the top experts in this area, these volumes will provide readers with an excellent overview of the current research in and applications of theta functions.

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