The authors study the differential geometry of lightlike (degenerated) submanifolds of codimension 2 of a semi-Riemannian manifold. Taking into account the degree of degeneration two classes of lightlike submanifolds are considered, half lightlike submanifolds and totally lightlike submanifolds. In each case Gauss formulae, Weingarten formulae are obtained; second fundamental forms, shape operators are defined. Some results about totally lightlike submanifolds are given, for instance Theorem 4: Any totally lightlike surface of a 4-dimensional semi- Riemannian manifold is totally geodesic.