  We present, in explicit matrix representation and a modernity befitting the
community, the classification of the finite discrete subgroups of G_2 and
compute the McKay quivers arising therefrom. Of physical interest are the
classes of N=1 gauge theories descending from M-theory and of mathematical
interest are possible steps toward a systematic study of crepant resolutions to
smooth G_2 manifolds as well as generalised McKay Correspondences. This writing
is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the
analogues for Calabi-Yau three- and four-folds were considered.
