We measure the gas-phase oxygen abundances of ~3000 star-forming galaxies at z=0.05-0.75 using optical spectrophotometry from the AGN and Galaxy Evolution Survey (AGES), a spectroscopic survey of I_AB<20.45 galaxies over 7.9 deg^2 in the NOAO Deep Wide Field Survey (NDWFS) Bootes field. We use state-of-the-art techniques to measure the nebular emission lines and stellar masses, and explore and quantify several potential sources of systematic error, including the choice of metallicity diagnostic, aperture bias, and contamination from unidentified active galactic nuclei (AGN). Combining volume-limited AGES samples in six independent redshift bins and ~75,000 star-forming galaxies with r_AB<17.6 at z=0.05-0.2 selected from the Sloan Digital Sky Survey (SDSS) that we analyze in the identical manner, we measure the evolution of the stellar mass-metallicity (M-Z) between z=0.05 and z=0.75. We find that at fixed stellar mass galaxies at z~0.7 have just 30%-60% the metal content of galaxies at the present epoch, where the uncertainty is dominated by the strong-line method used to measure the metallicity. Moreover, we find no statistically significant evidence that the M-Z relation evolves in a mass-dependent way for M=10^9.8-10^11 Msun star-forming galaxies. Thus, for this range of redshifts and stellar masses the M-Z relation simply shifts toward lower metallicity with increasing redshift without changing its shape.
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