  The hot big-bang cosmology provides a reliable accounting of the Universe
from about $10^{-2}\sec$ after the bang until the present, as well as a robust
framework for speculating back to times as early as $10^{-43}\sec$. Cosmology
faces a number of important challenges; foremost among them are determining the
quantity and composition of matter in the Universe and developing a detailed
and coherent picture of how structure (galaxies, clusters of galaxies,
superclusters, voids, great walls, and so on) developed. At present there is a
working hypothesis---cold dark matter---which is based upon inflation and
which, if correct, would extend the big bang model back to $10^{-32}\sec$ and
cast important light on the unification of the forces. Many experiments and
observations, from CBR anisotropy experiments to Hubble Space Telescope
observations to experiments at Fermilab and CERN, are now putting the cold dark
matter theory to the test. At present it appears that the theory is viable only
if the Hubble constant is smaller than current measurements indicate (around
$30\kms\Mpc^{-1}$), or if the theory is modified slightly, e.g., by the
addition of a cosmological constant, a small admixture of hot dark matter
($5\eV$ ``worth of neutrinos''), more relativistic particles, or a tilted
spectrum of density perturbations.
