We report the results of a worldwide campaign to observe WZ Sagittae during its 2001 superoutburst. After a 23-year slumber at V=15.5, the star rose within 2 days to a peak brightness of 8.2, and showed a main eruption lasting 25 days. The return to quiescence was punctuated by 12 small eruptions, of ~1 mag amplitude and 2 day recurrence time; these “echo outbursts” are of uncertain origin, but somewhat resemble the normal outbursts of dwarf novae. After 52 days, the star began a slow decline to quiescence. Periodic waves in the light curve closely followed the pattern seen in the 1978 superoutburst: a strong orbital signal dominated the first 12 days, followed by a powerful common superhump at 0.05721(5) d, 0.92(8)% longer than Porb. The latter endured for at least 90 days, although probably mutating into a “late” superhump with a slightly longer mean period [0.05736(5) d]. The superhump appeared to follow familiar rules for such phenomena in dwarf novae, with components given by linear combinations of two basic frequencies: the orbital frequency ωo and an unseen low frequency Ω, believed to represent the accretion disk’s apsidal precession. Long time series reveal an intricate fine structure, with ~20 incommensurate frequencies. Essentially all components occurred at a frequency nωo–mΩ, with m=1, ..., n. But during its first week, the common superhump showed primary components at nωo–Ω, for n=1, 2, 3, 4, 5, 6, 7, 8, 9 (i.e., m=1 consistently); a month later, the dominant power shifted to components with m=n–1. This may arise from a shift in the disk’s spiral-arm pattern, likely to be the underlying cause of superhumps. The great majority of frequency components are red-shifted from the harmonics of ωo, consistent with the hypothesis of apsidal advance (prograde precession). But a component at 35.42 c/day suggests the possibility of a retrograde precession at a different rate, probably N=0.13±0.02 c/day. The eclipses permit measuring the location and brightness of the mass-transfer hot spot. The disk must be very eccentric and nearly aslarge as the white dwarf’s Roche lobe. The hotspot luminosity exceeds its quiescent value by a factor of up to 60. This indicates that enhanced mass transfer from the secondary plays a major role in the eruption. (Refer to PDF file for exact formulas)