Three Dimensional Einstein-Weyl Geometry

This paper is an investigation of various differential geometric properties of three-dimensional Einstein-Weyl spaces. We show that, in a suitable gauge and coordinate system, these spaces are analytic. We find classes of explicit examples and we consider the behaviour of godesics in general and in some of these examples. Although most of the material is orginal, our intention is to be expository, and to compare and contrast the theory of Einstein-Weyl spaces with the theory of Einstein spaces.