This project will support the Workshop on Ergodic Theory and Symbolic Dynamics to be held from June 19 to July 14, 1989 at the University of Washington under the direction of Professor Douglas Lind. The workshop will focus on recent developments in ergodic theory and symbolic dynamics and will include the theories of restricted orbit equivalence and joinings as unifying themes in measurable ergodic theory, measurable and algebraic actions of certain groups, applications of symbolic dynamics to data transmission and storage and to the spectra of nonnegative matrices, and work relating complex analytic dynamics and automorphisms of symbolic systems. Ergodic theory has its origins in statistical and celestial mechanics and has since grown in many directions, drawing strength from subjects as diverse as Lie groups and number theory, while contributing to many other mathematical disciplines. There have been many interactions discovered between ergodic theory and symbolic dynamics.