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We have imaged five 7\arcmin \x 7\arcmin\ fields in M31 spanninggalactocentric radii from 4 to 32 kpc along the SW-major axis. The fields wereobserved through two broad-band (\V\ and \I) and two narrow-band (\CN\ and\TiO) filters. The broad-band data were used to construct \IvsVI\color-magnitude diagrams (CMDs) and, in some of our fields, we foundsignificant numbers of stars in the Cepheid instability strip. A distancemodulus for the Cepheids in the middle field was found that agreed well withother values in the literature values. The width of the giant branch (GB) inthe \IvsVI\ CMD of all 5 fields was investigated, and we show that in four ofthe fields a likely explanation for the GB width is a combination of {\it both}metallicity and mass variations. Using the broad-band data, the asymptoticgiant branch (AGB) luminosity functions (LFs) were measured in the five fields,and we show that differences exist between these LFs. We speculate on how thedifferent star forming histories in the fields may lead to the observed AGB LFsand GB widths. Using the narrow-band data along with the broad-band data weseparated the AGB stars into carbon-rich (C) and oxygen-rich (M) types. Thecarbon stars LFs were used to obtain an estimate for the distance modulus ofM31 which agrees with the value derived from Cepheids. The ratio of C- toM-stars (C/M) is believed to be an indicator of gaseous chemical abundance atthe time of formation of these stars. We show that the C/M ratio increasessmoothly with galactocentric distance, suggesting an inverse correlation withmetallicity. This is the first demonstration of this effect within a singleextragalactic system. We find that differences in the width of the GB and theAGB LFs do not significantly affect the C/M ratio. We consider the effect ofthe increasing C/M ratio on the ISM in M31, and cite evidence in favor of amodel where the grain composition in M31 is a function of galactocentricdistance.Comment: UUencoded compressed postscript, 3 Figs. available on request.  (Contact brewer@geop.ubc.ca

Late-Type Stars in M31. I. Photometric Study of AGB Stars and Metallicity Gradients