Cover13; -- Foreword13; -- Preface13; -- Contents13; -- Chapter 1 Preliminaries13; -- 1.1 n-Dimensional Space13; -- 1.2 Superscript and Subscript13; -- 1.3 The Einstein's Summation Convention13; -- 1.4 Dummy Index13; -- 1.5 Free Index13; -- 1.6 Kronecker Delta13; -- Exercises13; -- Chapter 2 Tensor Algebra13; -- 2.1 Introduction13; -- 2.2 Transformation of Coordinates13; -- 2.3 Covariant and Contravariant Vectors (Tensor of Rank One)13; -- 2.4 Contravariant Tensor of Rank Two13; -- 2.5 Covariant Tensor of Rank Two13; -- 2.6 Mixed Tensor of Rank Two13; -- 2.7 Tensor of Higher Order13; -- 2.8 Scalar or Invariant13; -- 2.9 Addition and Subtraction of Tensors13; -- 2.10 Multiplication of Tensors (Outer Product of Tensor)13; -- 2.11 Contraction of a Tensor13; -- 2.12 Inner Product of Two Tensors13; -- 2.13 Symmetric Tensors13; -- 2.14 Skew-Symmetric Tensor13; -- 2.15 Quotient Law13; -- 2.16 Conjugate (or Reciprocal) Symmetric Tensor13; -- 2.17 Relative Tensor13; -- Miscellaneous Examples 13; -- Exercises13; -- Chapter 3 Metric Tensor and Riemannian Metric13; -- 3.1 The Metric Tensor13; -- 3.2 Conjugate Metric Tensor: (Contravariant Tensor)13; -- 3.3 Length of a Curve13; -- 3.4 Associated Tensor13; -- 3.5 Magnitude of Vector13; -- 3.6 Scalar Product of Two Vectors13; -- 3.7 Angle Between Two Vectors13; -- 3.8 Angle Between Two Coordinate Curves13; -- 3.9 Hypersurface13; -- 3.10 Angle Between Two Coordinate Hypersurface13; -- 3.11 n-Ply Orthogonal System of Hypersurfaces13; -- 3.12 Congruence of Curves13; -- 3.13 Orthogonal Ennuple13; -- Miscellaneous Examples13; -- Exercises13; -- Chapter 4 Christoffel's Symbols and Covariant Differentiation13; -- 4.1 Christoffel's Symbols13; -- 4.2 Transformation of Christoffel's Symbols13; -- 4.3 Covariant Differentiation of a Covariant Vector13; -- 4.4 Covariant Differentiation of a Contravariant Vector13; -- 4.5 Covariant Differentiation of Tensors13; -- 4.6 Ricci's Theorem13; -- 4.7 Gradient, Divergence and Curl13; -- 4.8 The Laplacian Operator13; -- Exercises13; -- Chapter 5 Riemann-Christoffel Tensor13; -- 5.1 Riemann-Christoffel Tensor13; -- 5.2 Ricci Tensor13; -- 5.3 Covariant Riemann-Christoffel Tensor13; -- 5.4 Properties of Riemann-Christoffel Tensors of First Kind Rijkl -- 5.5 Bianchi Identity13; -- 5.6 Einstein Tensor13; -- 5.7 Riemann Curvature of a Vn13; -- 5.8 Formula for Riemannian Curvature in the Terms of Covariant curvature Tensor of Vn13; -- 5.9 Schurs Theorem -- 5.10 Mean Curvature13; -- 5.11 Riccis Principal Directions13; -- 5.12 Einstein Space13; -- 5.13 Weyl Tensor or Projective Curvature Tensor13; -- Exercises13; -- Chapter 6 The e-Systems and the Generalized Kronecker Deltas13; -- 6.1 Completely Symmetric13; -- 6.2 Completely Skew-Symmetric13; -- 6.3 e-System13; -- 6.4 Generalised Kr246;necker Delta13; -- 6.5 Contraction of i jk13; -- Exercises13; -- Chapter 7 Geometry13; -- 7.1 Length of Arc13; -- 7.2 Curvilinear Coordinates in E313; -- 7.3 Reciprocal Base Systems13; -- 7.4 On the Meaning of Covariant Derivatives13; -- 7.5 Intrinsic Differentiation13; -- 7.6 Parallel Vector Fields13; -- 7.7 Geo.