  It has recently been observed that MgB_2 is a superconductor with a high
transition temperature. Here we propose a model of anisotropic s-wave
superconductivity which consistently describes the observed properties of this
compound, including the thermodynamic and optical response in sintered MgB_2
wires. We also determine the shape of the quasiparticle density of states and
the anisotropy of the upper critical field and the superfluid density which
should be detectable once single-crystal samples become available.
