The study of non-transitive actions of a Lie group G on a smooth manifold is a very interesting problem. The first and most natural case is the case when the action is of cohomogeneity one . Many mathematicians have studied cohomogeneity one Riemannian G-manifolds and there are much nice result in the literature on the subject. But for the cohomogeneity one pseudo-Riemannian manifolds there are no much result in the literature. In this book, which is based on the Ph.D. thesis of the first author, we want to study these manifolds.