  Gravitational lensing directly measures mass density fluctuations along the
lines of sight to very distant objects. No assumptions need to be made
concerning bias, the ratio of fluctuations in galaxy density to mass density.
Hence, lensing is a very useful tool to study the universe at low to moderate
redshifts.
  We describe in detail a new method to trace light rays from redshift zero
through a three dimensional mass distribution to high redshift. As an example,
this method is applied here to a standard cold dark matter universe. We obtain
a variety of results, some of them statistical in nature, others from rather
detailed case studies of individual ``lines of sight". Among the former are the
frequency of multiply imaged quasars, the distribution of separation of the
multiple quasars, and the redshift distribution of lenses: all that as a
function of quasar redshift. We find effects from very weak lensing to highly
magnified multiple images of high redshift objects, which, for extended
background sources, (i.e. galaxies), range from slight deformations of the
shapes through tangentially aligned arclets up to giant luminous arcs.
  Different cosmological models differ, increasingly with redshift, in their
predictions for the mass (thus gravitational potential) distributions. Our
ultimate goal is to apply this method to a number of cosmogonic models and to
eliminate some models whose gravitational lensing properties are inconsistent
with those observed.
