For 1978/9 the Ring Theory Study Group at Bedford College rather naively set out to learn what had been done in the preceding decade on groups of cohomological dimension One. This is a particularly attractive subject, that has witnessed substantial success, essentially beginning in 1968 with results of Serre, Stallings and Swan, later receiving impetus from the introduction of the concept of the fundamental group of a connected graph of groups by Bass and Serre, and recently culminating in Dunwoody's contribution which completed the characterization.