The ‘Local Volume HI Survey’ (LVHIS) comprises deep H i spectral line and 20-cm radio continuum observations of 82 nearby, gas-rich galaxies, supplemented by multiwavelength images. Our sample consists of all galaxies with Local Group velocities vLG < 550 km s^-1 or distances D < 10 Mpc that are detected in the H i Parkes All Sky Survey (HIPASS). Using full synthesis observations in at least three configurations of the Australia Telescope Compact Array (ATCA), we obtain detailed H i maps for a complete sample of gas-rich galaxies with δ < ∼ - 30°. Here we present a comprehensive LVHIS galaxy atlas, including the overall gas distribution, mean velocity field, velocity dispersion and position-velocity diagrams, together with a homogeneous set f measured and derived galaxy properties. Our primary goal is to investigate the H i orphologies, kinematics and environment at high esolution and sensitivity. LVHIS alaxies represent a wide range of morphologies and sizes; our measured H i masses ange from ∼107 o 1010 M⊙, based n independent distance estimates. The LVHIS galaxy atlas (incl. FITS files) is available on-line.