This book contains 21 essays by leading authorities on aspects of contemporary logic, ranging from foundations of set theory to applications of logic in computing and in the theory of fields. In computer science and mathematics, this gap between foundations and applications is small, as illustrated by essays on the proof theory of non-classical logics, lambda calculus, relating logic programs to inductive definition, and definability in Lindenbaum algebras. Other chapters discuss how to apply model theory to field theory, complex geometry and groups, and how to recover from its automorphism group. W. A. Hodges, Professor, School of Mthematical Sciences, Queen Mary and Westfield College, University of London. J. M. E. Hyland, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge. C. I. Steinhorn, Department of Mathematics, Vassar College.