The theory of -trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of -trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmuller space for a finitely generated group using R-trees. In that work they were led to define the idea of a L-tree, where is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on R-trees, notably Rips' theorem on free actions. There has also been some advancement for certain other ordered abelian groups, including an interesting model-theoretic connection.

Introduction to -Trees will prove to be useful for mathematicians and research students in algebra and topology.