  Giant pulses are short, intense outbursts of radio emission with a power-law
intensity distribution that have been observed from the Crab Pulsar and PSR
B1937+21. We have undertaken a systematic study of giant pulses from PSR
B1937+21 using the Arecibo telescope at 430, 1420, and 2380 MHz. At 430 MHz,
interstellar scattering broadens giant pulses to durations of $\sim50 \mu$secs,
but at higher frequencies the pulses are very short, typically lasting only
$\sim1$-$2 \mu$secs. At each frequency, giant pulses are emitted only in narrow
($\lsim10 \mu$s) windows of pulse phase located $\sim 55$-$70 \mu$sec after the
main and interpulse peaks. Although some pulse-to-pulse jitter in arrival times
is observed, the mean arrival phase appears stable; a timing analysis of the
giant pulses yields precision competitive with the best average profile timing
studies. We have measured the intensity distribution of the giant pulses,
confirming a roughly power-law distribution with approximate index of -1.8,
contributing $\gsim0.1%$ to the total flux at each frequency. We also find that
the intensity of giant pulses falls off with a slightly steeper power of
frequency than the ordinary radio emission.
