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Galaxies are believed to interact with their surroundings via inflows and outflows of gas passing through the circumgalactic medium (CGM). Understanding the connections of galaxies to their CGM is therefore crucial for understanding galaxy evolution. I will report results from our  imaging and spectroscopic studies aimed at understanding how the CGM gas and dust properties correlate with the stellar properties of galaxies. In a study of star-forming galaxies at redshifts z < 0.14 located nearly "on top" of background quasars, based on HST COS, SDSS, and GBT spectroscopy of the quasars, we find a 100% detection rate of strong H I absorption. Using HST multi-band imaging, we measure the morphological and stellar properties of galaxies at 0.2 < z < 1.4 associated with gas-rich quasar absorbers and mapped with MUSE integral field spectroscopy. Most absorber galaxies seem to be consistent with the star formation main sequence (SFMS), while some lie below it, suggesting longer-than-typical gas-depletion timescales. Furthermore, we find that strong H I absorption may often trace larger-scale structures consisting of multiple galaxies. I will also report results from our HST COS observations for local (z < 0.1) galaxies with existing MaNGA integral field spectroscopy (IFS), which enable us to compare in detail the CGM gas properties with extrapolations of maps of gas velocity and metallicity in the inner ~1.5-2.5 effective radii of the galaxies. Combining our samples with the literature, we determine the radial profile of the H I gas and find it to agree overall with the predictions of hydrodynamical simulations. Surprisingly, we also find the H I column density to be anticorrelated with the stellar mass and galaxy size.  Comparing the kinematics, ionization, and metallicity of the CGM gas with the ionized gas in star-forming regions in the galaxies, we find consistency with a co-rotation of the cool CGM with galaxy disks and hints of changes in gas ionization as a function of galactocentric distance, potentially due to the stronger intergalactic radiation field at larger distances. Finally, I will report results from our JWST studies of the composition, structure, and extinction properties of the dust grains in both the diffuse and dense ISM/CGM of galaxies at 0<z<1.5, which indicate that dust grains in distant galaxies differ in physical and chemical properties from grains in local galaxies, with potential implications for dust extinction corrections for distant galaxies.