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 ^ { \prime } \times 17 ^ { \prime } region of M31 , with a detection limit of \sim 2 \times 10 ^ { 35 } \hbox { erg } \thinspace \hbox { s } ^ { -1 } .
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 \times 10 ^ { 37 } \hbox { erg } \thinspace \hbox { s } ^ { -1 } ) .
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 .