This book is about the study of manifolds with indefinite metrics. Since the concept of space-time in physics is endowed with indefinite metric and by combining space and time into a single manifold, various theories have been simplified, so the study of manifolds with indefinite metric has a great relevance towards the geometrization of Physics. In this context, various manifolds namely quasi-Kaehler manifolds, Kaehler manifolds and Sasakian manifolds, with indefinite metric, have been studied in this book. It also elaborates the concept of lightlike (degenerate) geometry of submanifolds. In this direction, CR lightlike submanifolds of an indefinite Kaehler manifold have been discussed and various results regarding mixed geodesic and mixed foliate CR- lightlike submanifolds have been established. This helps to define the induced geometric objects on the lightlike submanifolds which was not earlier possible by using the theory of non-degenerate submanifolds.