  The paper is a study of geodesic in two-dimensional pseudo-Riemannian
metrics. Firstly, the local properties of geodesics in a neighborhood of
generic parabolic points are investigated. The equation of the geodesic flow
has singularities at such points that leads to a curious phenomenon: geodesics
cannot pass through such a point in arbitrary tangential directions, but only
in certain directions said to be admissible (the number of admissible
directions is generically 1 or 3). Secondly, we study the global properties of
geodesics in pseudo-Riemannian metrics possessing differentiable groups of
symmetries. At the end of the paper, two special types of discontinuous metrics
are considered.
