  A wave-front in a space-time $\cal M$ is a family of null geodesics
orthogonal to a smooth spacelike two-surface in $\cal M$; it is of some
interest to know how a wave-front can fail to be a smoothly immersed surface in
$\cal M$. In this paper we see that the space of null geodesics $\cal N$ of
$\cal M$, considered as a contact manifold, provides a natural setting for an
efficient study of the stable singularities arising in the time evolution of
wave-fronts.

General Relativity and Quantum Cosmology