Nicholas M. Katz is professor of mathematics at Princeton University. He is the author or coauthor of six previous titles in the Annals of Mathematics Studies: "Arithmetic Moduli of Elliptic Curves "(with Barry Mazur); "Gauss Sums, Kloosterman Sums, and Monodromy Groups"; "Exponential Sums and Differential Equations"; "Rigid Local Systems"; "Twisted L-Functions and Monodromy;" and "Moments, Monodromy, and Perversity."