  This article provides the complete description of results from the Phase I
data set of the Sudbury Neutrino Observatory (SNO). The Phase I data set is
based on a 0.65 kt-year exposure of heavy water to the solar $^8$B neutrino
flux. Included here are details of the SNO physics and detector model,
evaluations of systematic uncertainties, and estimates of backgrounds. Also
discussed are SNO's approach to statistical extraction of the signals from the
three neutrino reactions (charged current, neutral current, and elastic
scattering) and the results of a search for a day-night asymmetry in the
$\nu_e$ flux. Under the assumption that the $^8$B spectrum is undistorted, the
measurements from this phase yield a solar $\nu_e$ flux of $\phi(\nu_e) =
  1.76^{+0.05}_{-0.05}{(stat.)}^{+0.09}_{-0.09} {(syst.)}
  \times 10^{6}$ cm$^{-2}$ s$^{-1}$, and a non-$\nu_e$ component
$\phi(\nu_{\mu\tau}) =
  3.41^{+0.45}_{-0.45}{(stat.)}^{+0.48}_{-0.45} {(syst.)}
  \times 10^{6}$ cm$^{-2}$ s$^{-1}$. The sum of these components provides a
total flux in excellent agreement with the predictions of Standard Solar
Models. The day-night asymmetry in the $\nu_e$ flux is found to be $A_{e} = 7.0
\pm 4.9 \mathrm{(stat.)^{+1.3}_{-1.2}}% \mathrm{(sys.)}$, when the asymmetry in
the total flux is constrained to be zero.
