  We employ the ADHM method to derive the moduli space of two instantons in
U(1) gauge theory on a noncommutative space. We show by an explicit
hyperK\"ahler quotient construction that the relative metric of the moduli
space of two instantons on $R^4$ is the Eguchi-Hanson metric and find a unique
threshold bound state. For two instantons on $R^3\times S^1$, otherwise known
as calorons, we give the asymptotic metric and conjecture a completion. We
further discuss the relationship of caloron moduli spaces of A, D and E groups
to the Coulomb branches of three dimensional gauge theory. In particular, we
show that the Coulomb branch of SU(2) gauge group with a single massive adjoint
hypermultiplet coincides with the above two caloron moduli space.
