The data sets presented here are used for the preparations of a 3-dimensional modelling of the gravity field in the Western Mediterranean/Ligurian Sea. As part of the AlpArray initiative and the German priority program MB-4D, various compilations of the gravity field are available: Bouguer and Free Air Anomaly, as well as variously calculated residual fields that provide new insight into crustal and lithospheric structures. The anomalies have been processed according to modern standards. The recalculations were part of the research of the international AlpArray Gravity Group. In particular, the residual fields in the area of the Ligurian Sea show hitherto unknown small-scale anomalies after subtraction of long-wave components (satellite gravimetry). The short wavelengths in the gravity field of different magnitudes suggest strong structuring of the lithosphere e.g., offshore Marseille (with an anomaly of about 60 mGal and in the areas between the French-Italian mainland and Corsica-Sardinia (with up to 100 mGal). Furthermore, the new compilations suggest that the crustal underground of this area is not formed by a uniform basin, but by domains of rather different densities. The Italian coastal region between Genoa and Livorno is characterized by a belt of positive anomalies (up to 60 mGal). The subsurface beneath the two islands of Corsica and Sardinia is characterized by strong negative anomalies in the residual field, indicating density deficits beneath. The new findings are supported by applications of Euler deconvolution, gradient methods, directional filters, and curvature calculations considering also the evaluation of GOCE gradients.