Maps of galactic HI, reconstructed from the HI4PI 21-cm line survey data (HI4PI Collaboration 2016, A&A 594, A116), Strasbourg astronomical Data Center, using a Bayesian variational inference approach. Here, we provide the mean and standard deviation of the gas density (in cm-3) on a three-dimensional 768\(\times\)768\(\times\)64 grid, spanning -24 kpc < x < 24 kpc, -24 kpc < y < 24 kpc and -2 kpc < z < 2 kpc, both for the BEG03 and the SBM15 gas flow models: HI_dens_mean_BEG03.fits HI_dens_stddev_BEG03.fits HI_dens_mean_SBM15.fits HI_dens_stddev_SBM15.fits In addition, we also publish the mean and standard deviation of the mass surface density (in Msun pc-2) on a two-dimensional 768\(\times\)768 grid, spanning -24 kpc < x < 24 kpc and -24 kpc < y < 24 kpc, again for both gas flow models: HI_surf_mass_dens_mean_BEG03.fits HI_surf_mass_dens_stddev_BEG03.fits HI_surf_mass_dens_mean_SBM15.fits HI_surf_mass_dens_stddev_SBM15.fits Throughout, we have assumed the optically thin limit for the gas and adopted the conversion factor \(X_{{\rm HI}}\simeq 1.823\times 10^{18}\) molecules cm-2 (K km s-1)-1. Refer to the FITS headers for more detailed information and see arXiv:2202.02341 for a detailed description of the reconstruction as well as a comparison with earlier studies. When using the deprojected gas maps in your research work, please refer to this Zenodo dataset and the following publication P. Mertsch and V.H.M. Phan, "Bayesian inference of three-dimensional gas maps: II. Galactic HI", arXiv:2202.02341.