he Swift Gamma-Ray Explorer is designed to make prompt multiwavelength observations of gamma-ray bursts (GRBs) and GRB afterglows. The X-ray telescope (XRT) enables Swift to determine GRB positions with a few arcseconds accuracy within 100 s of the burst onset. The XRT utilizes a mirror set built for JET-X and an XMM-Newton/EPIC MOS CCD detector to provide a sensitive broad-band (0.2-10 keV) X-ray imager with effective area of > 120 cm^sup 2^ at 1.5 keV, field of view of 23.6 × 23.6 arcminutes, and angular resolution of 18 arcseconds (HPD). The detection sensitivity is 2×10^sup -14^ erg cm^sup -2^ s^sup -1^ in 10^sup 4^ s. The instrument is designed to provide automated source detection and position reporting within 5 s of target acquisition. It can also measure the redshifts of GRBs with Fe line emission or other spectral features. The XRT operates in an auto-exposure mode, adjusting the CCD readout mode automatically to optimize the science return for each frame as the source intensity fades. The XRT will measure spectra and lightcurves of the GRB afterglow beginning about a minute after the burst and will follow each burst for days or weeks.PUBLICATION ABSTRACT