  We report the results of a deep spatial, spectral, and timing analysis of
ROSAT HRI and PSPC observations of the edge-on starburst galaxy NGC 253. In
this first paper, point-like X-ray sources detected within the galaxy and in
the field are discussed.
  In total, 73 X-ray sources have been collected in the NGC 253 field, 32 of
which are associated with the disk of the galaxy. Though 27 of these disk
sources are detected with the HRI (some being resolvable with the PSPC), the
remaining 5 PSPC-only detected sources are likely not to be real point sources,
being instead due to fluctuations within the X-ray structure of the disk. The
source close to the center of the galaxy is extended (L_x = 1e39 erg/s in the
ROSAT 0.1-2.4 keV band), and is most likely associated with the nuclear
starburst activity. The remaining sources have luminosities ranging from 7e36
erg/s to 3e38 erg/s, yielding an integrated point source luminosity of 1e39
erg/s.
  The halo of NGC 253 is filled with diffuse, filamentary X-ray emission. Seven
sources are located (or projected) in this diffuse emission region. Time
variability arguments, together with optical identifications, are put forward
to explain 4 sources as background objects, the other 3 sources likely being
spurious detections caused by local enhancements in the diffuse emission of the
halo of NGC 253. The diffuse X-ray emission components of NGC 253 will be
discussed in a separate paper.
