  We develop a theory of Einstein rings and demonstrate it using the infrared
Einstein ring images of the quasar host galaxies observed in PG1115+080,
B1608+656 and B1938+666. The shape of an Einstein ring accurately and
independently determines the shape of the lens potential and the shape of the
lensed host galaxy. We find that the host galaxies of PG1115+080, B1608+656 and
B1938+666 have axis ratios of 0.58+/-0.02, 0.69+/-0.02 and 0.62+/-0.15
including the uncertainties in the lens models. The Einstein rings break the
degeneracies in the mass distributions or Hubble constants inferred from
observations of gravitational lenses. In particular, the Einstein ring in
PG1115+080 rules out the centrally concentrated mass distributions that lead to
a high Hubble constant (H_0>60 km/s Mpc) given the measured time delays. Deep,
detailed observations of Einstein rings will be revolutionary for constraining
mass models and determining the Hubble constant from time delay measurements.
