Gamma-ray bursts (GRBs) are bright flashes of gamma-ray energy that originate in distant galaxies and last only a matter of seconds before fading away, never to appear again. They are accompanied by longer-wavelength "afterglows" that fade away much more gradually and can be detected for up to several days or even weeks after the gamma-ray burst has vanished.

In recent years, another phenomenon has been discovered that resembles gamma-ray bursts in almost every way, except that the radiated energy comes mostly from x-rays instead of gamma rays. This new class of bursts has been dubbed "x-ray flashes" (XRFs). There is strong evidence to suggest that GRBs and XRFs are closely-related phenomena.

The Swift mission, launched in November of 2004, is designed to answer many questions about GRBs and their cousins, XRFs--where they come from, what causes them, and why gamma-ray bursts and x-ray flashes differ. The key to the Swift mission is its ability to detect and determine the location of a burst in the sky and then autonomously point x-ray and optical telescopes at the burst position within seconds of the detection. This allows the measurement of the afterglow within 1 - 2 minutes after the burst, rather than several hours later, as was necessary with past missions. This early afterglow measurement is an important key to distinguishing between different theories that seek to explain the differences between XRFs and GRBs.

This dissertation describes the calibration of the Burst Alert Telescope, which measures the spectral and temporal properties of GRBs and XRFs. It also presents a study of XRFs and GRBs detected by Swift, including the first analysis and comparison of the early afterglow properties of these phenomena. This study reveals interesting differences between the temporal properties of GRB and XRF afterglows and sets strong constraints on some theories that seek to explain XRF origins.