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 for studying the universe at low to moderate redshifts. We describe in detail a new method for tracing 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 statistical results are the frequency of multiply imaged quasars, the distribution of separation of multiple quasars, and the redshift distribution of lenses, all as functions of quasar redshift. We find effects ranging from very weak lensing to highly magnified multiple images of high-redshift objects, which for extended background sources (i.e., galaxies) range from slight deformation of shape to tangentially aligned arclets to giant luminous arcs. Different cosmological models differ increasingly with redshift in their predictions of mass (and thus gravitational potential) distributions. Our ultimate goal is to apply this method to a number of cosmogonic models and to eliminate some models for which the gravitational lensing properties are inconsistent with those observed.
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