Historically one of the most important applications of orbifolds in geometric group theory has been to "triangles of groups". This is the simplest 2-dimensional example generalising the 1-dimensional "interval of groups" discussed in Serre's lectures on trees, where amalgamated free products are studied in terms of actions on trees. Such triangles of groups arise any time a discrete group acts simply transitively on the triangles in the affine Bruhat-Tits building for "SL"3(Qp); in 1979 Mumford discovered the first example for "p" = 2 (see below) as a step in producing an algebraic surface not isomorphic to projective space, but having the same Betti numbers. Triangles of groups were worked out in detail by Gersten and Stallings, while the more general case of complexes of groups, described above, was developed independently by Haefliger. The underlying geometric method of analysing finitely presented groups in terms of metric spaces of non-positive curvature is due to Gromov. In this context triangles of groups correspond to non-positively curved 2-dimensional simplicial complexes with the regular action of a group, transitive on triangles.