This paper reports on results of the analysis of the first M 31 survey with the ROSAT PSPC performed in July 1991. Within the =~ 6.3deg^2^ field of view we detected 396 individual X-ray sources with (0.1keV-2.4keV) fluxes ranging from =~ 5x10^-15^erg/cm^2^/s^ to =~ 4x10^-12^erg/cm^2^/s. Of these 396 sources, 43 have be en tentatively identified with foreground stars, 29 with globular clusters, 17 with supernova remnants, 3 with other galaxies (including M 32), and 3 with radio sources. A detailed analysis of the integral flux distribution of the sources shows that approximately one fifth are likely to be background objects. By comparison with the results of the Einstein M 31 survey, we find 327 newly detected sources, 15 moderately variable sources, 3 bright and 6 faint possible transient sources. For those sources in M 31, the observed luminosities range from =~ 3x10^35^erg/s to =~ 2x10^38^erg/s (at 690kpc). The total (0.1keV-2.4keV) luminosity of M 31 is (2.9+/-0.3)x10^39^erg/s, roughly one third of which is from the bulge and two thirds of which are from the disk. The luminosity of a diffuse component within the bulge region is estimated to be less than 3.2x10^38^erg/s. An explanation in terms of hot gaseous emission leads to a maximum total gas mass of 1.7x10^6^M_{sun}_. We find that the integral luminosity distribution of sources associated with globular clusters is similar to that of the Milky Way. Finally, the results of spectral fits to 56 of the brightest sources are discussed; we classify 15 objects as "supersoft sources" according to their spectral characteristics.
