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Observations from the Gravity Recovery and Interior Laboratory (GRAIL) mission indicate a marked change in the gravitational signature of lunar impact structures at the morphological transition, with increasing diameter, from complex craters to peak-ring basins. At crater diameters larger than ~200 km, a central positive Bouguer anomaly is seen within the innermost peak ring, and an annular negative Bouguer anomaly extends outward from this ring to the outer topographic rim crest. These observations demonstrate that basin-forming impacts remove crustal materials from within the peak ring and thicken the crust between the peak ring and the outer rim crest. A correlation between the diameter of the central Bouguer gravity high and the outer topographic ring diameter for well-preserved basins enables the identification and characterization of basins for which topographic signatures have been obscured by superposed cratering and volcanism. The GRAIL inventory of lunar basins improves upon earlier lists that differed in their totals by more than a factor of 2. The size-frequency distributions of basins on the nearside and farside hemispheres of the Moon differ substantially; the nearside hosts more basins larger than 350 km in diameter, whereas the farside has more smaller basins. Hemispherical differences in target properties, including temperature and porosity, are likely to have contributed to these different distributions. Better understanding of the factors that control basin size will help to constrain models of the original impactor population.