We present the Evolution of molecular Gas in Normal Galaxies ( EGNoG ) survey , an observational study of molecular gas in 31 star-forming galaxies from z = 0.05 to z = 0.5 , with stellar masses of ( 4 - 30 ) \times 10 ^ { 10 } M _ { \odot } and star formation rates of 4 - 100 M _ { \odot } yr ^ { -1 } . This survey probes a relatively un-observed redshift range in which the molecular gas content of galaxies is expected to have evolved significantly . To trace the molecular gas in the EGNoG galaxies , we observe the CO ( J = 1 \rightarrow 0 ) and CO ( J = 3 \rightarrow 2 ) rotational lines using the Combined Array for Research in Millimeter-wave Astronomy ( CARMA ) . We detect 24 of 31 galaxies and present resolved maps of 10 galaxies in the lower redshift portion of the survey . We use a bimodal prescription for the CO to molecular gas conversion factor , based on specific star formation rate , and compare the EGNoG galaxies to a large sample of galaxies assembled from the literature . We find an average molecular gas depletion time of 0.76 \pm 0.54 Gyr for normal galaxies and 0.06 \pm 0.04 Gyr for starburst galaxies . We calculate an average molecular gas fraction of 7-20 % at the intermediate redshifts probed by the EGNoG survey . By expressing the molecular gas fraction in terms of the specific star formation rate and molecular gas depletion time ( using typical values ) , we also calculate the expected evolution of the molecular gas fraction with redshift . The predicted behavior agrees well with the significant evolution observed from z \sim 2.5 to today .