We have mapped the structure and connectivity of the Shapley supercluster core and its surroundings as traced by its member galaxies. To achieve this, we have carried out a new redshift survey of galaxies across a 21 square degree region (17×17 Mpc2) of the Shapley supercluster containing 11 rich clusters, all lying at z ~ 0.048. This survey aims to provide full spectroscopic coverage of galaxies for the Shapley Supercluster Survey (ShaSS), a multiwavelength survey based on high-quality optical ugri and near-infrared K-band imaging acquired with the 2.6-m VST and 4.1-m VISTA telescopes. Targets were selected from the VST images as having i < 18.0 and WISE/W1 < 15.5 mag, and the observations were carried out with the AAOmega spectrograph on ...