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This book is focused on the general ideas on Contact Manifolds. A general introduction related to definition of Invariant Submanifolds, Sasakian, Kenmotsu and Trans-Sasakian manifolds, recurrence, bi-recurrence, generalized bi-recurrence, parallel third fundamental form, parallelism, bi- parallelism, Semiparallelism, bi-Semiparallelism, Pseudoparallelism, bi-Pseudoparallelism, Ricci-generalized pseudoparallelism, bi- Ricci-generalized pseudoparallelism and totally geodesic has been given in this book. Basic concept of Quarter symmetric-metric connection is also explained. This book definitely help the young researchers those who put step towards Invariant Submanifolds of Contact Manifolds and Invariant Submanifolds of Contact Manifolds admitting of Quarter symmetric-metric connection. Some example of 3 dimensional Sasakian and Trans-Sasakian manifolds are also proved in the other chapters of this book.