[en] We have made a comprehensive evaluation of the standard theory of primordial nucleosynthesis, by (a) determining the nuclear reactions most important for light element production in the Big Bang; (b) conducting a detailed study of the rates and uncertainties of these reactions (c) employing a Monte Carlo analysis to properly evaluate uncertainties in the computed elemental abundances arising from reaction rate uncertainties; and (d) comparing the predicted abundances of d, ³He, ⁴He, and ⁷Li to those inferred from observations. We find a consistent agreement for 2.68 x 10^-10 ≤ η ≤ 3.77 x 10^-10, where η is the baryon-to-photon ratio, thereby supporting the standard Big Bang nucleosynthesis (SBBN) theory. The corresponding constraint on the baryon density parameters is 0.01 ≤ Ω_b ≤ 0.09, where the primordial d+³He (⁴He) abundance sets the lower (upper) bound. We find that the new reaction rates increase the η upper bound from ⁷Li by 45%, and that inconsistencies in SBBN will arise if the primordial ⁴He mass fraction is less than 0.237 or if the primordial ⁷Li abundance is at the Pop I level. For slightly non-standard primordial nucleosynthesis models, comparisons to primordial abundances show that the number of neutrino families N_nu is limited to N_nu ≤ 3.3. Specifically, 3.5 neutrino families (3 Dirac ν's plus one Majorana ν) or more are ruled out at the 2-σ level. The dependence of the N_nu upper limit on the abundances limits has been parameterized