This clear concise and highly readable text Para-contact metric manifold deals with the study of various type of metric and non-metric connection in context of Para-contact manifolds. A brief introduction related to the definition of Differentiable manifold vector field and tangent space Lie-Bract Lie-derivatives covariant derivatives Exterior derivatives connection Riemannian manifold curvature tensor Almost contact metric manifold submanifolds and hypersurface has been given in this book. Certain curvature tensors like Quasi-conformal curvature tensor Pseudo projective curvature tensor G-projective curvature tensor etc are explained with P-Sasakian manifold. The characteristics properties of the different type of almost Para-contact metric manifold Almost Para-contact submanifolds and Hypersurfaces of almost product manifold are briefly discussed in this book.