T-theory: An Overview

T-theory is the name that we adopt for the theory of trees, injective envelopes of metric spaces, and all of the areas that are connected with these topics, which has been developed over the past 10–15 years in Bielefeld. Its motivation was originally—and still is to a large extent—the development of mathematical tools for reconstructing phylogenetic trees.T-theory expanded considerably when its relationships with the theory of affine buildings, valuated matroids, and decompositions of metrics were discovered. In this paper, we give a brief introduction to this theory, which we hope will serve as a useful reference to some of the main results, and also as a guide for further investigations into whatT-theory has to offer.