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In this paper we present a complete characterization of the first batch of Resistive AC-Coupled Silicon Detectors, called RSD1, designed at INFN Torino and manufactured by Fondazione Bruno Kessler (FBK) in Trento. With their 100% fill-factor, RSD represent the new enabling technology for high-precision 4D-tracking. Indeed, being based on the well-known charge multiplication mechanism of Low-Gain Avalanche Detectors (LGAD), they benefit from the very good timing performances of such technology together with an unprecedented resolution of the spatial tracking, which allows to reach the micron-level scale in the track reconstruction. This is essentially due to the absence of any segmentation structure between pads (100% fill-factor) and to other two innovative key-features: the first one is a properly doped n+ resistive layer, slowing down the charges just after being multiplied, and the second one is a dielectric layer grown on Silicon, inducing a capacitive coupling on the metal pads deposited on top of the detector. The very good spatial resolution (micron-level) we measured experimentally - higher than the nominal pad pitch - comes from the analogical nature of the readout of signals, whose amplitude attenuates from the pad center to its periphery, while the outstanding results in terms of timing (less than 14 ps, even better than standard LGAD) are due to a combination of very-fine pitch, analogical response and charge multiplication.