  D-brane technology and strong/weak coupling duality supplement traditional
orbifold techniques by making certain background geometries more accessible. In
this spirit, we consider some of the geometric properties of the type IIB
theory on R^6 \times M where M is an `Asymptotically Locally Euclidean (ALE)'
gravitational instanton. Given the self-duality of the theory, we can extract
the geometry (both singular and resolved) seen by the weakly coupled IIB string
by studying the physics of a D1-brane probe. The construction is both amusing
and instructive, as the physics of the probe completely captures the
mathematics of the construction of ALE instantons via `HyperKahler Quotients',
as presented by Kronheimer. This relation has been noted by Douglas and Moore
for the A-series. We extend the explicit construction to the case of the D- and
E-series -- uncovering a quite beautiful structure -- and highlight how all of
the elements of the mathematical construction find their counterparts in the
physics of the type IIB D-string. We discuss the explicit ALE metrics which may
be obtained using these techniques, and comment on the role duality plays in
relating gauged linear sigma models to conformal field theories.
