This collection of proceedings investigates the multifaceted and central role of theta functions across various mathematical disciplines. The authors, leading experts in the field, present research stemming from the 1987 AMS Summer Research Institute at Bowdoin College, offering an overview of current applications and theoretical advancements. The volumes explore connections between theta functions and semi-simple and nilpotent Lie group theory, quadratic forms, partition theory, statistical mechanics, quantum field theory, Riemann surfaces, abelian varieties, and solutions to differential equations in physics, thereby linking partial differential equations and algebraic geometry.

This two-volume collection is presented as a comprehensive overview of research on theta functions, drawing from a 1987 institute featuring top experts. The breadth of topics covered, from Lie group theory to quantum field theory and algebraic geometry, suggests a work of significant depth and interdisciplinary relevance. The collection is positioned to provide readers with an excellent understanding of the contemporary state of research and applications in this area.