  Quadruple gravitational lens systems offer the possibility of measuring time
delays for image pairs, microlensing effects, and extinction in distant
galaxies. Observations of these systems may be used to obtain estimates of H_o
and to study the various mass components of lens galaxies at high redshifts.
With HST, we have observed the reddest known gravitational lens system, MG
0414+0534. We used WFPC2/PC1 to obtain deep, high-resolution images with two
filters, F675W and F814W. We present a detailed analysis of all of the
components, as well as macrolens models. Our main results are: (1) confirmation
that MG 0414+0534 is inescapably a gravitational lens system; (2) discovery of
a blue arc connecting the 3 brightest images of the QSO central core; (3)
accurate positions and apparent brightnesses for all 4 known images of the QSO
central core and for the lens galaxy G; (4) a good representation of the
brightness distribution of G by elliptical isophotes with a De Vaucouleurs
profile, characteristic of an elliptical galaxy; (5) models that consist of
simple elliptical potentials and account qualitatively, not quantitatively, for
the HST image positions, arc morphology and radio flux ratios for the images of
the QSO central core; (6) a possible new test to distinguish between reddening
in the host galaxy of the QSO and in the lens galaxy, based on future accurate
measurements of spatial variations in the color of the arc; and (7) the
suggestion that microlensing is a plausible cause for the differences between
the radio and optical flux ratios for the brightest images, A1 and A2. Further
observations and measurements such as of the redshift of the lens galaxy, can
be used fruitfully to study microlensing for this system.
