  Warm dark matter (WDM) is an intriguing model of structure formation from the
point of view of both cosmology and particle physics. We consider a
one-parameter family of WDM models. The linear power spectra for these models
is calculated and compared with the corresponding spectra for cold dark matter
(CDM), hot dark matter (HDM) and mixed dark matter (MDM) as well as the power
spectrum derived from observations. Our linear analyses suggest that a model
universe dominated by a particle whose mass to temperature ratio $m_x/T_x$ is
increased by a factor of two as compared with the standard HDM neutrino gives a
reasonable fit to the data on large $(>8h^{-1} {\rm ~Mpc})$ scales. $N$-body
simulations for this particular WDM model show features of both HDM and CDM. As
in HDM, the first objects to collapse are large pancake-like structures. The
final matter distribution is rather smooth and structures as small as galaxy
halos are excluded. However, there appear to be virialized rich clusters
evident in the CDM but not the HDM simulations. Unfortunately, a simple
comparison of the matter distribution and its statistical properties with
observations indicates that WDM, like CDM, has too much power at small scales.
This is particularly evident in the small-scale pairwize velocity dispersion.
The cluster multiplicity function has the wrong shape with too many rich
clusters being produced, though this conclusion is based on the simple
assumption that light traces mass in groups of galaxies.
