We have obtained a deep 8-field XMM-Newton mosaic of M33 covering the galaxy out to the D$_{25}$ isophote and beyond to a limiting 0.2--4.5 keV unabsorbed flux of 5$times$10$^{-16}$ erg cm$^{-2}$ s$^{-1}$ (L${>}$4$times$10$^{34}$ erg s$^{-1}$ at the distance of M33). These data allow complete coverage of the galaxy with high sensitivity to soft sources such as diffuse hot gas and supernova remnants. Here we describe the methods we used to identify and characterize 1296 point sources in the 8 fields. We compare our resulting source catalog to the literature, note variable sources, construct hardness ratios, classify soft sources, analyze the source density profile, and measure the X-ray luminosity function. As a result of the large effective area of XMM-Newton below 1 keV, the survey contains many new soft X-ray sources. The radial source density profile and X-ray luminosity function for the sources suggests that only $sim$15% of the 391 bright sources with L${>}$3.6$times$10$^{35}$ erg s$^{-1}$ are likely to be associated with M33, and more than a third of these are known supernova remnants. The log(N)--log(S) distribution, when corrected for background contamination, is a relatively flat power-law with a differential index of 1.5, which suggests many of the other M33 sources may be high-mass X-ray binaries. Finally, we note the discovery of an interesting new transient X-ray source, which we are unable to classify.
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