  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 $z_{\rm abs}<$0.85
strong absorbers with measured N$_{HI}$ $\geq 10^{18}$ cm$^{\rm -2}$ from
UV-spectroscopy. We additionally use a new complementary HST medium program to
characterise 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
characterisation 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.
