  This study represents the most sensitive Chandra X-ray point source catalogue
of M31. Using 133 publicly available Chandra ACIS-I/S observations totalling ~1
Ms, we detected 795 X-ray sources in the bulge, northeast, and southwest fields
of M31, covering an area of approximately 0.6 deg$^{2}$, to a limiting
unabsorbed 0.5-8.0 keV luminosity of $10^{34}$ erg/s. In the inner bulge, where
exposure is approximately constant, X-ray fluxes represent average values
because they were determined from many observations over a long period of time.
Similarly, our catalogue is more complete in the bulge fields since monitoring
allowed more transient sources to be detected. The catalogue was
cross-correlated with a previous XMM-Newton catalogue of M31's $D_{25}$
isophote consisting of 1948 X-ray sources, with only 979 within the field of
view of our survey. We found 387 (49%) of our Chandra sources (352 or 44%
unique sources) matched to within 5 arcsec of 352 XMM-Newton sources. Combining
this result with matching done to previous Chandra X-ray sources we detected
259 new sources in our catalogue. We created X-ray luminosity functions (XLFs)
in the soft (0.5-2.0 keV) and hard (2.0-8.0 keV) bands that are the most
sensitive for any large galaxy based on our detection limits.
Completeness-corrected XLFs show a break around $1.3\times10^{37}$ erg/s,
consistent with previous work. As in past surveys, we find the bulge XLFs are
flatter than the disk, indicating a lack of bright high-mass X-ray binaries in
the disk and an aging population of low-mass X-ray binaries in the bulge.
