  We analyse deep multi-colour Advanced Camera images of the largest known
gravitational lens, A1689. Radial and tangential arcs delineate the critical
curves in unprecedented detail and many small counter-images are found near the
center of mass. We construct a flexible light deflection field to predict the
appearance and positions of counter-images. The model is refined as new
counter-images are identified and incorporated to improve the model, yielding a
total of 106 images of 30 multiply lensed background galaxies, spanning a wide
redshift range, 1.0$<$z$<$5.5. The resulting mass map is more circular in
projection than the clumpy distribution of cluster galaxies and the light is
more concentrated than the mass within $r<50kpc/h$. The projected mass profile
flattens steadily towards the center with a shallow mean slope of
$d\log\Sigma/d\log r \simeq -0.55\pm0.1$, over the observed range,
r$<250kpc/h$, matching well an NFW profile, but with a relatively high
concentration, $C_{vir}=8.2^{+2.1}_{-1.8}$. A softened isothermal profile
($r_{core}=20\pm2$\arcs) is not conclusively excluded, illustrating that
lensing constrains only projected quantities. Regarding cosmology, we clearly
detect the purely geometric increase of bend-angles with redshift. The
dependence on the cosmological parameters is weak due to the proximity of
A1689, $z=0.18$, constraining the locus, $\Omega_M+\Omega_{\Lambda} \leq 1.2$.
This consistency with standard cosmology provides independent support for our
model, because the redshift information is not required to derive an accurate
mass map. Similarly, the relative fluxes of the multiple images are reproduced
well by our best fitting lens model.
