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The book is intended to serve as a reference book for new research scholars those who want to work in the field of Differential Geometry of Manifolds. The purpose in writing the book has been to provide a development of the genegeneralized almost contact manifolds and their submanifolds which is well-motivated, rigorous and not painful to understand. In modern analysis the geometry of submanifolds have become a subject of growing interest for its significant application in applied mathematics and theoretical physics. For instance, the notion of invariant submanifold is used to discuss properties of non-linear autonomous system. Also the notion of geodesics plays an important role in the theory of relativity. For totally geodesic submanifolds, the geodesics of the ambient manifolds remain geodesics in the submanifolds. Hence, totally geodesic submanifolds have also importance in physical science.