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During the week of September 13, 1988 the Mathematical Sciences Research Institute hosted a four day workshop on Arboreal Group Theory. This volume is the product of that meeting. The program centered on the topic of the theory of groups acting on trees and the various applications to hyperbolic geometry. Topics include the theory of length functions, structure of groups acting freely on trees, spaces of hyperbolic structures and their compactifications, and moduli for tree actions.