We present interferometric CO observations, made with the Combined Array for Millimeter-wave Astronomy (CARMA) interferometer, of galaxies from the Extragalactic Database for Galaxy Evolution survey (EDGE). These galaxies are selected from the Calar Alto Legacy Integral Field Area (CALIFA) sample, mapped with optical integral field spectroscopy. EDGE provides good-quality CO data (3σ sensitivity {{{Σ }}}{mol}∼ 11 {M}ȯ {{pc}}-2 before inclination correction, resolution ∼1.4 kpc) for 126 galaxies, constituting the largest interferometric CO survey of galaxies in the nearby universe. We describe the survey and data characteristics and products, then present initial science results. We find that the exponential scale lengths of the molecular, stellar, and star-forming disks are approximately equal, and galaxies that are more compact in molecular gas than in stars tend to show signs of interaction. We characterize the molecular-to-stellar ratio as a function of Hubble type and stellar mass and present preliminary results on the resolved relations between the molecular gas, stars, and star-formation rate. We then discuss the dependence of the resolved molecular depletion time on stellar surface density, nebular extinction, and gas metallicity. EDGE provides a key data set to address outstanding topics regarding gas and its role in star formation and galaxy evolution, which will be publicly available on completion of the quality assessment.