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The distribution of gas and metals in the circumgalactic medium (CGM) plays a critical role in how galaxies evolve. The MUSE-ALMA Haloes survey combines MUSE, ALMA, and HST observations to constrain the properties of the multiphase gas in the CGM and the galaxies associated with the gas probed in absorption. In this paper, we analyse the properties of galaxies associated with 32 strong ${\rm H\, {\small I}}$ Ly-α absorbers at redshift 0.2 ≲ z ≲ 1.4. We detect 79 galaxies within ±500 kms−1 of the absorbers in our 19 MUSE fields. These associated galaxies are found at physical distances from 5.7 kpc and reach star formation rates as low as 0.1 M⊙ yr−1. The significant number of associated galaxies allows us to map their physical distribution on the Δv and b plane. Building on previous studies, we examine the physical and nebular properties of these associated galaxies and find the following: (i) 27/32 absorbers have galaxy counterparts and more than 50 per cent of the absorbers have two or more associated galaxies, (ii) the ${\rm H\, {\small I}}$ column density of absorbers is anticorrelated with the impact parameter (scaled by virial radius) of the nearest galaxy as expected from simulations, (iii) the metallicity of associated galaxies is typically larger than the absorber metallicity, which decreases at larger impact parameters. It becomes clear that while strong ${\rm H\, {\small I}}$ absorbers are typically associated with more than a single galaxy, we can use them to statistically map the gas and metal distribution in the CGM.

The gas cycling in the circumgalactic regions of galaxies is known to be multi-phase. The MUSE–ALMA Haloes survey gathers a large multi-wavelength observational sample of absorption and emission data with the goal to significantly advance our understanding of the physical properties of such CGM gas. A key component of the MUSE–ALMA Haloes survey is the multi-facility observational campaign conducted with VLT/MUSE, ALMA, and HST. MUSE–ALMA Haloes targets comprise 19 VLT/MUSE IFS quasar fields, including 32 zabs <0.85 strong absorbers with measured N(H i) ≥1018 cm−2 from UV-spectroscopy. We additionally use a new complementary HST medium program to characterize the stellar content of the galaxies through a 40-orbit three-band UVIS and IR WFC3 imaging. Beyond the absorber-selected targets, we detect 3658 sources all fields combined, including 703 objects with spectroscopic redshifts. This galaxy-selected sample constitutes the main focus of the current paper. We have secured millimeter ALMA observations of some of the fields to probe the molecular gas properties of these objects. Here, we present the overall survey science goals, target selection, observational strategy, data processing and source identification of the full sample. Furthermore, we provide catalogues of magnitude measurements for all objects detected in VLT/MUSE, ALMA, and HST broad-band images and associated spectroscopic redshifts derived from VLT/MUSE observations. Together, this data set provides robust characterization of the neutral atomic gas, molecular gas and stars in the same objects resulting in the baryon census of condensed matter in complex galaxy structures.