  We describe and discuss the global properties of 45 gamma-ray bursts (GRBs)
observed by HETE-2 during the first three years of its mission, focusing on the
properties of X-Ray Flashes (XRFs) and X-ray-rich GRBs (XRRs). We find that the
numbers of XRFs, XRRs, and GRBs are comparable. We find that the durations and
the sky distributions of XRFs and XRRs are similar to those of GRBs. We also
find that the spectral properties of XRFs and XRRs are similar to those of
GRBs, except that the values of the peak energy $E^{\rm obs}_{\rm peak}$ of the
burst spectrum in $\nu F_\nu$, the peak energy flux $\Fp$, and the energy
fluence $S_E$ of XRFs are much smaller -- and those of XRRs are smaller -- than
those of GRBs. Finally, we find that the distributions of all three kinds of
bursts form a continuum in the [$S_E$(2-30 keV),$S_E$(30-400) keV]-plane, the
[$S_E$(2-400 keV), $E_{\rm peak}$]-plane, and the [$F_{\rm peak}$(50-300 keV),
$E_{\rm peak}$]-plane. These results provide strong evidence that all three
kinds of bursts arise from the same phenomenon.
