  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
P_orb. 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 omega_o and an unseen low frequency Omega, 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 n(omega_o)-m(Omega), with m=1, ..., n. But
during its first week, the common superhump showed primary components at n
(omega_o)-Omega, 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 ... . (etc., abstract continues)
