  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.
