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.