Big-bang nucleosynthesis is one of the cornerstones of the standard
cosmology. For almost thirty years its predictions have been used to test the
big-bang model to within a fraction of a second of the bang. The concordance
that exists between the predicted and observed abundances of D, 3He, 4He
and 7Li provides important confirmation of the standard cosmology and leads
to the most accurate determination of the baryon density, between 1.7 \times
10^{-31}\gcmm3 and 4.1\times 10^{-31}\gcmm3 (corresponding to between about
1\% and 14\% of critical density). This measurement of the density of ordinary
matter is crucial to almost every aspect of cosmology and is pivotal to the
establishment of two dark-matter problems: (i) most of the baryons are dark,
and (ii) if the total mass density is greater than about 14\% of the critical
density as many determinations now indicate, the bulk of the dark matter must
be ``nonbaryonic,'' comprised of elementary particles left from the earliest
moments. We critically review the present status of primordial nucleosynthesis
and discuss future prospects.Comment: 21 pages+6 figs, LaTeX(2.09), FERMILAB-Pub-94/174-A, Figures
available by anonymous ftp in oddjob.uchicago.edu:/pub/bbnrev/fig?.ps
(?=1,2,3,4,5,6) or email from [email protected] REVISIONS include new
discussion and a new figur