Machine derived contents note: The Einstein Summation Convention. -- Basic Linear Algebra for Tensors. -- General Tensors. -- Tensor Operations. -- Tests for Tensor Character. -- The Metric Tensor. -- The Derivative of a Tensor. -- Further Riemannian Geometry. -- Riemannian Curvature. -- Spaces of Zero Curvature. -- Tensors in Differential Geometry. -- Tensors in Mechanics. -- Tensors in Special Relativity. -- Tensors Without Coordinates. -- Introduction to Tensor Manifolds