Lays the foundation for a theory of uniformization of p -adic hyperbolic curves and their moduli. On one hand, the theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedean places. On the other hand, the theory may be regarded as a fairly precise hyperbolic analogue of the Serre-Tate theory of ordinary abelian varieties and their moduli. In some sense, the book is a continuation and generalization of A Theory of Ordinary p-adic Curves , 1996, written by the same author. Annotation c. Book News, Inc., Portland, OR (booknews.com)