  We report on \chandra observations of the central region of M31. By combining
eight \chandra ACIS-I observations taken between 1999 and 2001, we have
identified 204 X-ray sources within the central $\sim 17'\times17'$ region of
M31, with a detection limit of $\sim 2\times10^{35}$\lum. Of these 204 sources,
22 are identified with globular clusters, 2 with supernova remnants, 9 with
planetary nebula, and 9 as supersoft sources. By comparing individual images,
about 50% of the sources are variable on time scales of months. We also found
13 transients, with light curves showing a variety of shapes. We also extracted
the energy spectra of the 20 brightest sources; they can be well fit by a
single power-law with a mean photon index of 1.8. The spectral shapes of 12
sources are shown to be variable, suggesting that they went through state
changes. The luminosity function of all the point sources is consistent with
previous observations (a broken power-law with a luminosity break at
$1.7\times10^{37}$\lum). However, when the X-ray sources in different regions
are considered separately, different luminosity functions are obtained. This
indicates that the star-formation history might be different in different
regions.
