  We analyze stable homology over associative rings and obtain results over
Artin algebras and commutative noetherian rings. Our study develops similarly
for these classes; for simplicity we only discuss the latter here.
  Stable homology is a broad generalization of Tate homology. Vanishing of
stable homology detects classes of rings---among them Gorenstein rings, the
original domain of Tate homology. Closely related to gorensteinness of rings is
Auslander's G-dimension for modules. We show that vanishing of stable homology
detects modules of finite G-dimension. This is the first characterization of
such modules in terms of vanishing of (co)homology alone.
  Stable homology, like absolute homology, Tor, is a theory in two variables.
It can be computed from a flat resolution of one module together with an
injective resolution of the other. This betrays that stable homology is not
balanced in the way Tor is balanced. In fact, we prove that a ring is
Gorenstein if and only if stable homology is balanced.
