Cluster Mass Reconstruction by a Weak Shear Field

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