  The developments summarized with the name ``weak gravitational lensing'' have
led to exciting possibilities to study the (statistical properties of the) dark
matter distribution in the Universe. Concentrating on those aspects which
require deep wide-field imaging surveys, we describe the basic principles of
weak lensing and discuss its future applications in view of NGST (a) to
determine the statistical properties of the dark matter halos of individual
galaxies, (b) to determine the mass and the mass profile of very low-mass
clusters and groups at medium redshift and/or of more massive clusters at very
high redshift, and (c) to measure the power spectrum of the matter distribution
in the Universe in the non-linear regime, thereby also obtaining a
mass-selected sample of halos and providing a means to investigate the scale-
and redshift dependence of the bias `factor'.
