  We report on the detection of dark matter in the cluster Abell 2218 using the
weak gravitational distortion of background galaxies. We find a highly
significant, coherent detection of the distortion in the images of the
background galaxies. The inferred 2D mass distribution has a peak that is
coincident with the optical and X-ray centroid. The qualitative distributions
of the cluster light, the X-ray emission and the dark matter are similar and
the projected total mass, gas, and light surface densities are consistent with
a $r^{-1}$ profile at distance of $r > 180^{\prime\prime}$ from the cluster cD
galaxy. Using the weak lensing technique, we determine a lower bound for the
total mass in A2218 of $(3.9 \pm 0.7) \times 10^{14}$~h$^{-1}$~M$_\odot$ within
a fiducial aperture of radius 0.4~h$^{-1}$Mpc. The associated cluster
mass-to-light ratio is $(440 \pm 80)$~h~$M_\odot/L_{\odot B}$. The mass
estimated by the weak lensing method is consistent with that inferred from the
X-ray data under the assumption of hydrostatic equilibrium and we derive an
upper bound for the gas-to-total mass ratio at 400~h$^{-1}$kpc of
$M_{gas}/M_{tot} = (0.04 \pm 0.02)$h$^{-3/2}$.
