  We present a systematic analysis of the three-flavor
Mikheyev-Smirnov-Wolfenstein (MSW) oscillation solutions to the solar neutrino
problem, in the hypothesis that the two independent neutrino square mass
differences, $\delta m^2$ and $m^2$, are well separated: $\delta m^2 \ll m^2$.
At zeroth order in $\delta m^2/m^2$, the relevant variables for solar neutrinos
are $\delta m^2$ and two mixing angles, $\omega$ and $\phi$. We introduce new
graphical representations of the parameter space $(\delta
m^2,\,\omega,\,\phi)$, that prove useful both to analyze the properties of the
electron-neutrino survival probability and to present the results of the
analysis of solar neutrino data. We make a detailed comparison between the
theoretical predictions of the Bahcall--Pinsonneault standard solar model and
the current experimental results on solar neutrino rates, and discuss
thoroughly the MSW solutions found by spanning the whole three-flavor space
$(\delta m^2,\,\omega,\,\phi)$. The allowed regions can be radically different
from the usual ``small mixing'' and ``large mixing'' solutions, characteristic
of the usual two-generation MSW approach. We also discuss the link between
these results and the independent information on neutrino masses and mixings
coming from accelerator and reactor oscillation searches.
