Cluster mass reconstruction by a weak shear field

The tidal gravitational field of galaxy clusters causes a coherent distorti on of the images of background sources. Since the distribution of image dis tortions, namely the shear field, traces the local gravitational potential of a deflector, it can be used to reconstruct the two-dimensional mass dist ribution of clusters of galaxies. Moreover, the shear field can provide uni que information on the redshift distribution of high-redshift galaxies. In this review we summarize recently-developed parameter-free methods of clust er-mass reconstruction based on the shear field, and we apply a mass-recons truction method to the cluster Abell 370 at redshift 0.375.