This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are "semi-symmetric spaces foliated by Euclidean leaves of codimension two" in the sense of Z I Szab . The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of "relative conullity two". This makes a bridge to a...