Differential Geometry of Lightlike Submanifolds This is the first systematic account of the main results in the theory of lightlike submanifolds of semi Riemannian manifolds which have a geometric structure such as almost Hermitian almost contact metric or quaternion Kähler. Using these structures the book presents interesting classes of submanifolds whose geometry is very rich. The book also includes hypersurfaces of semi Riemannian manifolds their use in general relativity and Osserman geometry half lightlike submanifolds of semi Riemannian manifolds lightlike submersions screen conformal submersions and their applications in harmonic maps. Basic constructions and definitions are presented as preliminary background in every chapter. The presentation explores applications and suggests several open questions. This self contained monograph provides up to date research in lightlike geometry and is intended for graduate students and researchers just entering this field. This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian Sasakian and quaternion Kähler manifolds.