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The ALMaQUEST (ALMA-MaNGA QUEnching and STar formation) survey is a programwith spatially-resolved $^{12}$CO(1-0) measurements obtained with the AtacamaLarge Millimeter Array (ALMA) for 46 galaxies selected from the Mapping NearbyGalaxies at Apache Point Observatory (MaNGA) DR15 optical integral-fieldspectroscopic survey. The aim of the ALMaQUEST survey is to investigate thedependence of star formation activity on the cold molecular gas content at kpcscales in nearby galaxies. The sample consists of galaxies spanning a widerange in specific star formation rate (sSFR), including starburst (SB),main-sequence (MS), and green valley (GV) galaxies. In this paper, we presentthe sample selection and characteristics of the ALMA observations, and showcasesome of the key results enabled by the combination of spatially-matched stellarpopulations and gas measurements. Considering the global (aperture-matched)stellar mass, molecular gas mass, and star formation rate of the sample, wefind that the sSFR depends on both the star formation efficiency (SFE) and themolecular gas fraction ($f_{\rm H_{2}}$), although the correlation with thelatter is slightly weaker. Furthermore, the dependence of sSFR on the moleculargas content (SFE or $f_{\rm H_{2}}$) is stronger than that on either the atomicgas fraction or the molecular-to-atomic gas fraction, albeit with the small HIsample size. On kpc scales, the variations in both SFE and $f_{\rm H_{2}}$within individual galaxies can be as large as 1-2 dex thereby demonstratingthat the availability of spatially-resolved observations is essential tounderstand the details of both star formation and quenching processes.

ALMaQUEST -- IV. The ALMA-MaNGA QUEnching and STar formation (ALMaQUEST) Survey