  (abridged) Aims: RXS J113155.4-123155 (z=0.66) is a quadruply imaged lensed
quasar with a resolved Einstein Ring. The goal of this paper is to provide a
full characterization of this system, and more particularly accurate astrometry
and photometry.
  Method: Visible and near-infrared imaging observations of RXS
J113155.4-123155 were carried out at various epochs using several ground based
telescopes and the HST. The frames have been deconvolved using the MCS
algorithm. A Singular Isothermal Ellipsoid (SIE) + external shear has been used
to model the lensing galaxy potential.
  Results: MCS deconvolution enables us to separate the flux of the QSO
(point-like images) from that of its host galaxy and to accurately track the
flux variations of the point-like images in various filters. The deconvolved
frames unveil several multiply imaged structures in the Einstein ring and an
unidentified object in the vicinity of the lensing galaxy. We discuss the
lightcurves and the chromatic flux ratio variations and deduce that both
intrinsic variability and microlensing took place during a span longer than one
year.
  We demonstrate that microlensing may easily account for the so called
anomalous flux ratios presented in the discovery paper. However, the observed
flux ratios are still poorly reproduced when modeling the lens potential with a
SIE+shear. We argue that this disagreement can hardly be explained by
milli-lensing caused by substructures in the lensing galaxy. A solution
proposed in Paper II consists in a more complex lens model including an
octupole term to the lens gravitational potential.
