The X-ray Telescope (XRT), on board the Swift satellite, provides: automated source detection and position with few arcsecond accuracy within few seconds from target acquisition; CCD spectroscopy and imaging capability (0.2-10 keV), with the capability of detecting a milliCrab source in about 10 seconds; automatic adjusting of the CCD readout mode to optimize the science return as the source fades. Swift main scientific goal is the study of gamma-ray burst (GRBs). XRT can observe GRB afterglows over several orders of magnitude in flux. The first results obtained during the first ten months of operation confirm that XRT is fully compliant with the requirements and is providing excellent results. In particular it is detecting a very steep decay in the early X-ray light curve of many afterglows. Often there are also strong flares superimposed to the X-ray light curve, probably related to the continued internal engine activity. XRT is also localising for the first time the X-ray counterparts to short bursts.