The Book Semi-invariant Submanifolds with certain connections is explores the study of semi-invariant submanifolds with some connections like semi symmetric, non metric, quarter symmetric, non metric and semi symmetric semi-metric and quarter symmetric semi-metric connections of manifold equipped with certain distinguished structures. The structures such as Sasakian, nearly Sasakian , trans Sasakian, nearly trans Sasakian and Kenmotsu manifold is one of the most interesting topic in the differential geometry of the manifolds. In a manifold with an almost contact metric structure, the (1, 1) structure vector field transforms a vector into a vector perpendicular to it. Thus it becomes a natural motivation to study submanifold of a manifold with almost contact metric structure, according to the behavior of its tangent bundle under the action of the (1, 1) structure vector field of the ambient manifold. There are two well known classes of submanifolds, namely invariant submanifolds and anti-invariant submanifolds. In the first case the tangent spaces of the sub-manifolds remains invariant .