We present an overview of a multi-wavelength survey of the Shapley supercluster (SSC; z~0.05) covering a contiguous area of 260 h^-2_70 Mpc^2 including the supercluster core. The project main aim is to quantify the influence of cluster-scale mass assembly on galaxy evolution in one of the most massive structures in the local Universe. The Shapley supercluster survey (ShaSS) includes nine Abell clusters (A3552, A3554, A3556, A3558, A3559, A3560, A3562, AS0724, AS0726) and two poor clusters (SC1327- 312, SC1329-313) showing evidence of cluster-cluster interactions. Optical (ugri) and near-infrared (K) imaging acquired with VST and VISTA allow us to study the galaxy population down to m*+6 at the supercluster redshift. A dedicated spectroscopic survey with AAOmega on the Anglo-Australian Telescope provides a magnitude-limited sample of supercluster members with 80% completeness at ~m*+3. We derive the galaxy density across the whole area, demonstrating that all structures within this area are embedded in a single network of clusters, groups and filaments. The stellar mass density in the core of the SSC is always higher than 9E09 M_sun Mpc^-3, which is ~40x the cosmic stellar mass density for galaxies in the local Universe. We find a new filamentary structure (~7 Mpc long in projection) connecting the SSC core to the cluster A3559, as well as previously unidentified density peaks. We perform a weak-lensing analysis of the central 1 sqdeg field of the survey obtaining for the central cluster A3558 a mass of M_500=7.63E14 M_sun, in agreement with X-ray based estimates.