  We extend previous studies of the physics of interstellar cloud collisions by
beginning investigation of the role of magnetic fields through 2D
magnetohydrodynamic (MHD) numerical simulations. We study head-on collisions
between equal mass, mildly supersonic diffuse clouds. We include a moderate
magnetic field and two limiting field geometries, with the field lines parallel
(aligned) and perpendicular (transverse) to the colliding cloud motion. We
explore both adiabatic and radiative cases, as well as symmetric and asymmetric
ones. We also compute collisions between clouds evolved through prior motion in
the intercloud medium and compare with unevolved cases.
  We find that: In the (i) aligned case, adiabatic collisions, like their HD
counterparts, are very disruptive, independent of the cloud symmetry. However,
when radiative processes are taken into account, partial coalescence takes
place even in the asymmetric case, unlike the HD calculations. In the (ii)
transverse case, collisions between initially adjacent unevolved clouds are
almost unaffected by magnetic fields. However, the interaction with the
magnetized intercloud gas during the pre-collision evolution produces a region
of very high magnetic energy in front of the cloud. In collisions between
evolved clouds with transverse field geometry, this region acts like a
``bumper'', preventing direct contact between the clouds, and eventually
reverses their motion. The ``elasticity'', defined as the ratio of the final to
the initial kinetic energy of each cloud, is about 0.5-0.6 in the cases we
considered. This behavior is found both in adiabatic and radiative cases.
