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Star formation activity plays a key role in driving galaxy evolution, and it depends on the amount of cold gas available (as traced by CO emission) and on the physical conditions and dynamical state of this gas. This work focuses on investigating the star formation efficiency of the gas, both molecular and total, as a function of local and global galaxy properties. The galaxy samples studied in this thesis are representative of the nearby universe, and we use a combination of interferometric CO observations and integral field unit optical spectroscopy for most of our analyses.

First, we show that in a sample of galaxies dominated by ``field galaxies'' the disk scale lengths for the molecular and stellar components are very similar, reflecting the close relation between CO emission and star formation activity. Our analysis of the radial dependence of the star formation efficiency of the total gas on morphological, structural, and dynamical properties of the galaxies shows that there is a smooth, continuous exponential decline with increasing radius (mostly driven by the increased contribution of atomic gas), and a systematic increase in the average gas efficiency from early to late type galaxies. Our results also show a morphological dependence of the efficiency per orbital time, which may reflect star formation quenching due to the presence of a bulge.

Next, we test the impact of environmental processes on galaxies immersed in the rich environment of the Virgo cluster. We show that in these galaxies the CO emission is more centrally concentrated than the stars, unlike what we saw in the field. Moreover, in the central regions of galaxies with an increasing level of perturbation (as determined by the morphology and kinematics of their atomic gas emission), the mean molecular-to-atomic gas ratio increases while the star formation efficiency of the molecular gas in the same region decreases. This demonstrates that the cluster environment not only affects the outskirts of galaxy disks and their atomic gas, but deeply changes the distribution and efficiency of the centrally located molecular gas component.

Finally, we study the onset of star formation cessation in galaxies (quenching'') by investigating a complete sample of galaxies spanning from the main sequence (normal star forming objects) to the green valley (galaxies which are starting to quench) to the red cloud (galaxies that are mostly quiescent, that is, red and dead'' objects). We find that the star formation activity and the molecular gas-to-stellar mass ratio track each other. We also note that green valley galaxies have lower molecular star formation efficiencies than galaxies on the main sequence. On average, we find that within the bulges of green valley galaxies the molecular gas star formation efficiency is lower than in main sequence galaxies. Also in green valley galaxies, we find that the molecular gas to stellar ratio, the molecular gas star formation efficiency, and the specific star formation rate all increase with increasing distance to the center. Our results suggest that gas depletion or removal does not fully explain the star-formation quenching in galaxies transiting through the green valley, and that a reduction in star formation efficiency is also required during this stage. This is reminiscent of the so-called ``morphological quenching.''