  High angular resolution images of the complex gravitational lens system RXS
J1131-1231 (a quadruply imaged AGN with a bright Einstein ring) obtained with
the Advanced Camera for Surveys and NICMOS instruments onboard the Hubble Space
Telescope are analysed to determine the lens model and to reconstruct the host
galaxy.
  Results: 1- Precise astrometry and photometry of the four QSO lensed images
(A-D) and of the lensing galaxy (G) are obtained. They are found in agreement
with an independent study presented in a companion paper. The position and
colours of the X object seen in projection close to the lens are found to be
only compatible with a satellite galaxy associated with the lens.
  2- The Singular Isothermal Ellipsoid plus external shear provides a good fit
of the astrometry of images A-D. The positions of extended substructures are
also well reproduced. However an octupole (m=4) must be added to the lens
potential in order to reproduce the observed lens position, as well as the
IB/IC point-like image flux ratio. The ellipticity and orientation of the mass
quadrupole are found similar to those of the light distribution, fitted by a
Sersic profile. The lens (z=0.295) is found to be a massive elliptical in a
rich environment and showing possible evolution with respect to z=0.
  3- The host galaxy (z=0.658) is found to be a substantially magnified (M ~ 9)
luminous Seyfert 1 spiral galaxy. The angular resolution is sufficient to see
regions where stars are intensively forming. Interaction with a closeby
companion is also observed.
  4- Finally, in the case of RXS J1131-1231, extended lensed structures do not
help much in constraining the lens model.
