A theory of sonoluminescence has been developed based on the compression and eventual ionization of air in a bubble by the converging shock waves generated by the applied acoustic radiation. The air is compressed to such high densities that departures from the ideal gas law become very significant. An extension to the van der Waals gas has been made to the similarity theory of Guderley for the structure of spherical shocks in an ideal gas. The linear stability of these shocks has also been examined.