Because gravitational lensing effects operate on all scales, it provides a way to estimate the total mass and possibly its distribution from the innermost to the outermost regions of clusters of galaxies. In fact, large arcs provide the most robust estimation of the total mass in the center ( 10-100 h50-1 kpc), with almost no a priori hypothesis on the dynamical state of the cluster. At large distances, the weakly distorted sources can be studied individually or statistically. They provide the gradient and the geometrical shape of the distribution of the total mass. It is therefore not surprising that most of the immediate issues arising from gravitational arc(let)s concern the mass distribution and the mass function of the dark matter in clusters of galaxies: arc(let)s are really a unique way to study the largest gravitationally bound systems in the universe, both from the point of view of the formation of large scale structures, or their internal dynamics and interactions between the different components of the cluster medium.
As compared with the modeling of multiply imaged QSOs, the rapid progress made in modeling the cluster potentials comes from the large angular scale of the image configuration, currently 10 to 100 times larger than the angular resolution of the optical images. The positions and shapes of the gravitational images of extended objects are well defined and give accurate constraints for the modeling of the lens. As well, the number of events already observed (cf part 3) is large and each new case benefits somewhat from the modeling of previous ones.
With deep CCD images, up to B = 27, the grid of distant background galaxies is so dense that it can be used to probe the potential of intermediate redshift clusters (z 0.1-0.5) with a spatial sampling of about 10 arcsec. Therefore, with the weak lensing effect the potential can be mapped up to about 5 h50-1 Mpc from the center of a rich cluster with a resolution better than 1 arcmin (Kaiser & Squire 1993, Bonnet, Mellier & Fort 1994, Smail et al. 1994b, Fahlman et al. 1994). When it will be possible to detect a dense population of background sources at redshifts as large as 1.5 or 2, it will be possible to study clusters at large distances (z 1-1.5).
The perturbations of caustic lines by dark matter halos of small size can produce mini-lensing effects of substructures of the sources. These can be used to probe the granularity of the mass distribution along the line of sight in the range 106 - 1012 solar masses. All of these possibilities motivate the strong efforts which are being done with the largest telescopes to observe arc(let)s in rich clusters. In fact complete modeling of clusters can only be done for observations of peculiar arc(let)s configurations that probe both the very inner part of the cluster as well as the periphery. Even so, some geometrical configurations of gravitational images are better for modeling than others (Kochanek 1992), and it is particularly important to select them among a large systematic survey. This was the first objective of the Toulouse arc survey (ESO-CFHT Key Programme), which provided interesting results on the distribution of cluster masses within about 100-200 h50-1 kpc from their center. Some of the most significant results, are presented below.