We develop a theory of Einstein rings and demonstrate it using the infrared Einstein ring images of the quasar host galaxies observed in PG 1115+080 , B 1608+656 and B 1938+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 PG 1115+080 , B 1608+656 and B 1938+666 have axis ratios of 0.58 \pm 0.02 , 0.69 \pm 0.02 and 0.62 \pm 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 PG 1115+080 rules out the centrally concentrated mass distributions that lead to a high Hubble constant ( H _ { 0 } > 60 km s ^ { -1 } Mpc ^ { -1 } ) 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 .