In this book, we consider Weyl spaces of dimension and pay attention to some properties that curvatures satisfy. By importing some additional structures, such as almost complex, almost Kaehlerian and almost -structures we broaden geometrical concepts of the spaces and examine the symmetry properties of these quantities. Similar to the Riemannian case the prolonged covariant derivative is defined, so that the prolonged covariantly constant quantities will be mentioned. As a special case, Einstein-Weyl space which has a certain type of Ricci curvature is examined. By starting the study of a prolongedly covariance concept, we are able to obtain generalized Einstein equation in Weyl spaces. That is, an Einstein -Weyl tensor is defined which is constant under prolonged covariant differentiation. In this book, we present the concepts and calculations so that the readers can follow them quite easily.