Manifolds and Submanifolds Reviewed

We begin with a brief review of differentiable manifolds, vector and tensor fields. Next, we brief on algebra and exterior derivation of differential forms, followed by linear connection and curvature tensor. Later, we briefly introduce the semi-Riemannian metric, its Levi-Civita connection and curvature tensors. Then we recall the basic notion and equations of submanifolds of semi-Riemannian manifolds. Finally, we present basic concepts and formulas of warped products.