  Galaxies and galaxy groups located along the line of sight towards
gravitationally lensed quasars produce high-order perturbations of the
gravitational potential at the lens position. When these perturbation are too
large, they can induce a systematic error on $H_0$ of a few-percent if the lens
system is used for cosmological inference and the perturbers are not explicitly
accounted for in the lens model. In this work, we present a detailed
characterization of the environment of the lens system WFI2033-4723 ($z_{\rm
src} = 1.662$, $z_{\rm lens}$ = 0.6575), one of the core targets of the H0LICOW
project for which we present cosmological inferences in a companion paper (Rusu
et al. 2019). We use the Gemini and ESO-Very Large telescopes to measure the
spectroscopic redshifts of the brightest galaxies towards the lens, and use the
ESO-MUSE integral field spectrograph to measure the velocity-dispersion of the
lens ($\sigma_{\rm {los}}= 250^{+15}_{-21}$ km/s) and of several nearby
galaxies. In addition, we measure photometric redshifts and stellar masses of
all galaxies down to $i < 23$ mag, mainly based on Dark Energy Survey imaging
(DR1). Our new catalog, complemented with literature data, more than doubles
the number of known galaxy spectroscopic redshifts in the direct vicinity of
the lens, expanding to 116 (64) the number of spectroscopic redshifts for
galaxies separated by less than 3 arcmin (2 arcmin) from the lens. Using the
flexion-shift as a measure of the amplitude of the gravitational perturbation,
we identify 2 galaxy groups and 3 galaxies that require specific attention in
the lens models. The ESO MUSE data enable us to measure the
velocity-dispersions of three of these galaxies. These results are essential
for the cosmological inference analysis presented in Rusu et al. (2019).
