  We examine in detail how BBN theory is constrained, and what predictions it
can make, when using only the most model-independent observational constraints.
We avoid the uncertainties and model-dependencies that necessarily arise when
solar neighborhood D and \he3 abundances are used to infer primordial D and
\he3 via chemical and stellar evolution models. Instead, we use \he4 and \li7,
thoroughly examining the effects of possible systematic errors in each. Via a
likelihood analysis, we find near perfect agreement between BBN theory and the
most model-independent data. Given this agreement, we then {\it assume} the
correctness of BBN to set limits on the single parameter of standard BBN, the
baryon-to-photon ratio, and to predict the primordial D and \he3 abundances. We
also repeat our analysis including recent measurements of D/H from quasar
absorption systems and find that the near perfect agreement between theory and
observation of the three isotopes, D, \he4 and \li7 is maintained. These
results have strong implications for the chemical and stellar evolution of the
light elements, in particular for \he3. In addition, our results (especially if
the D/H measurements are confirmed) have implications for the stellar depletion
of \li7. Finally, we set limits on the number \nnu\ of neutrino flavors, using
an analysis which carefully and systematically includes all available
experimental constraints. The value \nnu = 3.0 fits best with BBN and a 95\% CL
upper limit of \nnu $\la 4$ is established.
