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The present book has involved from the teaching of the course on Tensor Analysis by the post graduate and engineering students of Mathematics and Physics in various Universities of India. It deals with the Kronecker delta, Contravariant and Covariant tensors, Symmetric tensors, Quotient law of tensors, Relative tensor, Riemannian space, Metric tensor, Indicator, Permutation symbols and Permutation tensors. A detailed study of Christoffel symbols and their properties, Covariant differentiation of tensors, Ricci's theorem, Intrinsic derivative, Geodesics, Differential equation of geodesic, Geodesic coordinates, Field of parallel vectors, Reimann-Christoffel tensor and its properties, Covariant curvature tensor, Einstein space, Bianchi's identity, Einstein tensor, Flate space, Isotropic point and Schur's theorem with some other important theorems and examples from its concluding chapter.