A 50.4 ks ROSAT Position Sensitive Proportional Counter image of the n
earby spiral galaxy M33 reveals 37 sources within 15' of the nucleus b
righter than 7 x 10(35) ergs s(-1). There are at least 13 additional s
ources farther from the nucleus, most of which are likely to be associ
ated with M33 as well. Most of the bright sources that had been detect
ed with Einstein in the same region are still visible. The bulk of the
sources in the galaxy are associated with Population I tracers. Sever
al of the sources are time variable. There are 10 sources in the image
that lie within 20 '' of optically identified supernova remnants (SNR
s) in M33. The spectra of these sources are soft compared with most ot
her sources of comparable brightness, and therefore it is likely that
most of these X-ray sources are SNRs. Based on the identification of s
ources in M33, it appears likely that ROSAT hardness ratios of this ty
pe can be used to separate SNRs and compact sources in other nearby no
rmal galaxies as well. The northern and the southern spiral arms of M3
3 appear as diffuse features in the X-ray image. There is additional d
iffuse (or unresolved source) emission throughout the inner portions o
f M33. The diffuse emission is softer than the faint point sources and
the SNRs in the survey, and is well fitted in terms of a bremsstrahlu
ng spectrum with kT similar to 0.4 keV and log N-H similar to 20.6.