We describe the hCOSMOS redshift survey of the COSMOS field conducted with the Hectospec spectrograph on the MMT .
In the central 1 deg ^ { 2 } , the hCOS20.6 subset of the survey is > 90 \% complete to a limiting r = 20.6 .
The hCOSMOS survey includes 1701 new redshifts in the COSMOS field .
We also use the total of 4362 new and remeasured objects to derive the age sensitive D _ { n } 4000 index over the entire redshift interval 0.001 \lesssim z \lesssim 0.6 .
For 85 \% of the quiescent galaxies in hCOS20.6 , we measure the central line-of-sight velocity dispersion .
To explore potential uses of this survey , we combine previously measured galaxy sizes , profiles and stellar masses with the spectroscopy .
The comparison reveals the known relations among structural , kinematic , and stellar population properties .
We also compare redshift and D _ { n } 4000 distributions of hCOS20.6 galaxies with SHELS ; a complete spectroscopic survey of 4 deg ^ { 2 } observed to the same depth .
The redshift distributions in the two fields are very different but the D _ { n } 4000 distribution is remarkably similar .
The relation between velocity dispersion and stellar mass for massive hCOS20.6 galaxies is consistent with the local relation from SDSS .
Using measured velocity dispersions , we test a photometric proxy calibrated to galaxies in the local universe .
The systematic differences between the measured and photometric proxy velocity dispersions are correlated with galaxy dynamical and stellar population properties highlighting the importance of direct spectroscopic measurements .