This paper reports the results of the analysis of the second ROSAT PSPC survey of M31 performed in summer 1992. We compare our results with those of the first survey. Within the ~10.7 deg^2 field of view, 396 individual X-ray sources are detected in the second survey data, of which 164 are new detections. When combined with the first survey, this result in a total of 560 X-ray sources in the field of M31. Their (0.1 keV - 2.0 keV) fluxes range from 7 x 10^-15 to 7.6 x 10^-12 erg cm^-2 s^-1, and of these 560 sources, 55 are tentatively identified with foreground stars, 33 with globular clusters, 16 with supernova remnants, and 10 with radio sources and galaxies (including M32). A comparison with the results of the Einstein M31 survey reveals 491 newly detected sources, 11 long term variable sources, and 7 possible transient sources. Comparing the two ROSAT surveys, we come up with 34 long term variable sources and 8 transient candidates. For the M31 sources, the observed luminosities range from 4 x 10^35 to 4 x 10^38 erg s^-1. The total (0.1 keV - 2.0 keV) luminosity of M31 is (3.4+-0.3) x 10^39 erg s^-1, distributed approximately equally between the bulge and disk. Within the bulge region, the luminosity of a possible diffuse component combined with faint sources below the detection threshold is (2.0+-0.5) x 10^38 erg s^-1. An explanation in terms of hot gaseous emission leads to a maximum total gas mass of (1.0+-0.3) x 10^6 M_sun.
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