  In this paper we detail the lattice constructions of several classes of
supersymmetric quiver gauge theories in two and three Euclidean spacetime
dimensions possessing exact supersymmetry at finite lattice spacing. Such
constructions are obtained through the methods of topological twisting and
geometric discretization of Euclidean Yang--Mills theories with eight and
sixteen supercharges in two and three dimensions. We detail the lattice
constructions of two-dimensional quiver gauge theories possessing four and
eight supercharges and three-dimensional quiver gauge theories possessing eight
supercharges.
