| Preface | p. vii |
| Sources of Tensor Calculus | p. ix |
| Introduction | p. xv |
| Tensor Algebra | p. 1 |
| Local Basis Vectors. Jacobian and Metric Matrices | p. 1 |
| Vector Product | p. 12 |
| Geometric Definition of a Tensor and Algebraic Operations on Tensors | p. 17 |
| Algebra of Tensor Fields | p. 34 |
| Eigenvalues of a Tensor | p. 40 |
| Symmetric, Skew-Symmetric and Orthogonal Tensors | p. 43 |
| Physical Components of Tensors | p. 50 |
| Tensors of Higher Orders | p. 53 |
| Pseudotensors | p. 59 |
| Tensors in Linear Spaces | p. 65 |
| Linear n-Dimensional Space | p. 65 |
| Matrices of the nth Order | p. 74 |
| Linear Transformations of n-Dimensional Spaces | p. 85 |
| Dual Space | p. 93 |
| Algebra of Tensors in n-Dimensional Linear Spaces | p. 98 |
| Outer Forms | p. 116 |
| Groups of Transformations | p. 129 |
| Linear Transformations of Coordinates | p. 129 |
| Transformation Groups in Three-Dimensional Euclidean Space | p. 142 |
| Symmetry of Finite Bodies | p. 146 |
| Matrix Representation of Transformation Groups | p. 164 |
| Indifferent Tensors and Invariants | p. 169 |
| Indifferent Tensors | p. 169 |
| A Number of Independent Components for Indifferent Tensors | p. 180 |
| Symmetric Indifferent Tensors | p. 192 |
| Scalar Invariants | p. 202 |
| Invariants of Symmetric Second-Order Tensors | p. 212 |
| Tensor Functions | p. 227 |
| Linear Tensor Functions | p. 227 |
| Scalar Functions of a Tensor Argument | p. 253 |
| Potential Tensor Functions | p. 265 |
| Quasilinear Tensor Functions | p. 274 |
| Spectral Resolutions of Second-Order Tensors | p. 283 |
| Spectral Resolutions of Quasilinear Tensor Functions | p. 298 |
| Nonpotential Tensor Functions | p. 310 |
| Differentiation of a Tensor Function with respect to a Tensor Argument | p. 325 |
| Scalar Functions of Several Tensor Arguments | p. 328 |
| Tensor Functions of Several Tensor Arguments | p. 342 |
| Tensor Analysis | p. 347 |
| Covariant Differentiation | p. 347 |
| Differentiation of Second-Order Tensors | p. 357 |
| Properties of Covariant Derivatives | p. 361 |
| Covariant Derivatives of the Second Order | p. 367 |
| Differentiation in Orthogonal Curvilinear Coordinates | p. 372 |
| Geometry of Curves and Surfaces | p. 385 |
| Curves in Three-Dimensional Euclidean Space | p. 385 |
| Surfaces in Three-Dimensional Euclidean Space | p. 394 |
| Curves on a Surface | p. 413 |
| Geometry in a Vicinity of a Surface | p. 426 |
| Planar Surfaces in R[superscript 3] | p. 432 |
| Tensors in Riemannian Spaces and Affinely Connected Spaces | p. 437 |
| Riemannian Spaces | p. 437 |
| Affinely Connected Spaces | p. 448 |
| Riemannian Affinely Connected Spaces | p. 456 |
| The Riemann-Christoffel Tensor | p. 462 |
| Integration of Tensors | p. 475 |
| Curvilinear Integrals of Tensors | p. 475 |
| Surface Integrals of Tensors | p. 483 |
| Volume Integrals of Tensors | p. 488 |
| Tensors in Continuum Mechanics | p. 493 |
| Deformation Theory | p. 493 |
| Velocity Characteristics of Continuum Motion | p. 508 |
| Co-rotational Derivatives | p. 516 |
| Mass, Momentum and Angular Momentum Balance Laws | p. 524 |
| Thermodynamic Laws | p. 538 |
| The Deformation Compatibility Equation | p. 546 |
| The Complete System of Continuum Mechanics Laws | p. 553 |
| Tensor Functions in Continuum Mechanics | p. 555 |
| Energetic and Quasienergetic Couples of Tensors | p. 555 |
| General Principles for Tensor Functions in Continuum Mechanics | p. 572 |
| The Material Indifference Principle | p. 582 |
| The Material Symmetry Principle | p. 600 |
| Tensor Functions for Nonlinear Elastic Continua | p. 618 |
| Tensor Functions for Nonlinear Hypoelastic Continua | p. 646 |
| References | p. 653 |
| Subject Index | p. 655 |
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