  We report results from a multi-wavelength monitoring campaign on Mrk 421 over
the period of 2003-2004. The source was observed simultaneously at TeV and
X-ray energies, with supporting observations frequently carried out at optical
and radio wavelengths. The large amount of simultaneous data has allowed us to
examine the variability of Mrk 421 in detail. The variabilities are generally
correlated between the X-ray and gamma-ray bands, although the correlation
appears to be fairly loose. The light curves show the presence of flares with
varying amplitudes on a wide range of timescales both at X-ray and TeV
energies. Of particular interest is the presence of TeV flares that have no
coincident counterparts at longer wavelengths, because the phenomenon seems
difficult to understand in the context of the proposed emission models for TeV
blazars. We have also found that the TeV flux reached its peak days before the
X-ray flux during a giant flare in 2004. Such a difference in the development
of the flare presents a further challenge to the emission models. Mrk 421
varied much less at optical and radio wavelengths. Surprisingly, the normalized
variability amplitude in optical seems to be comparable to that in radio,
perhaps suggesting the presence of different populations of emitting electrons
in the jet. The spectral energy distribution (SED) of Mrk 421 is seen to vary
with flux, with the two characteristic peaks moving toward higher energies at
higher fluxes. We have failed to fit the measured SEDs with a one-zone SSC
model; introducing additional zones greatly improves the fits. We have derived
constraints on the physical properties of the X-ray/gamma-ray flaring regions
from the observed variability (and SED) of the source. The implications of the
results are discussed. (Abridged)
