  We have identified 127 discrete sources in a Chandra observation of M83, with
a detection limit of ~ 3 x 10^{36} erg/s in the 0.3-8.0 keV band. We discuss
the individual properties of about 20 bright sources with L_x >~ 10^{38} erg/s,
and the statistical properties of the whole sample. About 1/3 of the bright
sources show X-ray spectra with a bb component at kT <~ 1 keV, plus a p-law
component with Gamma ~ 2.5, typical of X-ray binaries (XRBs) in a soft state;
another third have p-law spectra with Gamma ~ 1.5, consistent with XRBs in a
hard state. Two bright sources show emission lines on a hard p-law continuum,
and are probably XRBs surrounded by a photo-ionized nebula or stellar wind.
Among the other bright sources, we also identified two SNR candidates, with
optically-thin thermal plasma spectra at kT ~ 0.5 keV. The two brightest
supersoft sources have T_bb ~ 70 eV and L_x ~ 10^{38} erg/s. Two candidate
X-ray pulsars are detected with periods ~ 200 s. Another source corresponds to
the core of a background FRII radio galaxy. The discrete sources can be divided
into three groups, based on their spatial, color and luminosity distributions.
The first group comprises supersoft sources with no detected emission above 1
keV. The second group consists of soft sources with little or no detected
emission above 2 keV. They are strongly correlated with H-alpha emission in the
spiral arms and starburst nucleus, tracing a young population. Their relative
abundance depends on the current level of star-formation. Most of them are
likely to be SNRs. The sources in the third group are mostly XRBs (in a soft or
hard state), reaching higher X-ray luminosities than sources in the other two
groups. Being a mixture of old low-mass and young high-mass systems, the whole
group appears to be of intermediate age when correlated with H-alpha.
