[en] Aims. 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. Methods. The lens model is constrained by the relative astrometric positions of the lens and point-like images, and by the extended lensed structures. The non-parametric light distribution is recovered in the source plane by means of back ray-tracing. 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 I-B/I-C 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 similar to 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.