  (Abridged) The galaxy cluster Abell 2218, at z=0.171, is well-known for the
discrepancy between mass estimates derived from X-ray and strong lensing
analyses. With the present XMM observation, we trace the gas density and
temperature profiles out to a radius of ~ 1400 h_70^-1 kpc (approximately the
virial radius of the cluster). The surface brightness profile is well fitted
over three orders of magnitude with a beta model, with a core radius of 0.'95
and \beta=0.63. The projected temperature profile declines steeply with radius
(by ~50%), and is well described by a polytrope with parameters t_0=8.09 keV
and \gamma=1.15. The temperature map shows a pronounced peak in the central
arcminute, with an increase of a factor of two (from ~5 to ~10 keV). The mass
profile, calculated assuming hydrostatic equilibrium and spherical symmetry, is
best fitted with a King approximation to an isothermal sphere, implying a dark
matter distribution with a central core, in contrast with the cusped cores
found in more obviously relaxed clusters. The X-ray mass is two times less than
the strong lensing mass at r ~ 80 h_50^-1 kpc, although the agreement between
X-ray and weak lensing mass measurements at larger radius (r ~ 400 h_50^-1 kpc)
is slightly better. While the X-ray total mass estimates can vary by 30%
depending on the mass model, all measurements are lower than the corresponding
total mass from optical measurements. Given the X-ray results indicating
disturbance of the intracluster gas, leading to a likely violation of the
assumption of hydrostatic equilibrium, and the observed substructure in the
optical, suggesting a line-of-sight merger, it is unlikely that the different
mass estimates of this cluster can be reconciled, at least with standard
modelling assumptions.
