  In an XMM-Newton raster observation of the bright Local Group spiral galaxy M
33 we study the population of X-ray sources (X-ray binaries, supernova
remnants) down to a 0.2--4.5 keV luminosity of 10^35 erg/s -- more than a
factor of 10 deeper than earlier ROSAT observations. EPIC hardness ratios and
optical and radio information are used to distinguish between different source
classes. The survey detects 408 sources in an area of 0.80 square degree. We
correlate these newly detected sources with earlier M 33 X-ray catalogues and
information from optical, infra-red and radio wavelengths. As M 33 sources we
detect 21 supernova remnants (SNR) and 23 SNR candidates, 5 super-soft sources,
and 2 X-ray binaries (XRBs). There are 267 sources classified as hard, which
may either be XRBs or Crab-like SNRs in M 33 or background AGN. The 44
confirmed and candidate SNRs more than double the number of X-ray detected SNRs
in M 33. 16 of these are proposed as SNR candidates from the X-ray data for the
first time. On the other hand, there are several sources not connected to M 33:
five foreground stars, 30 foreground star candidates, 12 active galactic
nucleus candidates, one background galaxy and one background galaxy candidate.
Extrapolating from deep field observations we would expect 175 to 210
background sources in this field. This indicates that about half of the sources
detected are sources within M 33.
