Note: Intro -- Teleparallel Gravity -- Preface -- Contents -- Chapter 1: Basic Notions -- 1.1 Linear Frames and Tetrads -- 1.1.1 Trivial Frames -- 1.1.2 Nontrivial Frames -- 1.2 Lorentz Connections -- 1.3 Curvature and Torsion -- 1.4 Local Lorentz Transformations -- 1.5 Bianchi Identities -- 1.6 Levi-Civita Symbol -- 1.7 Torsion Decomposition -- References -- Chapter 2: Lorentz Connections and Inertia -- 2.1 Purely Inertial Connection -- 2.2 Particle Equation of Motion -- 2.3 Four-Acceleration and Parallel Transport -- 2.4 Inertial Effects -- References -- Chapter 3: Gauge Theories and Gravitation -- 3.1 The Gauge Tenets -- 3.1.1 Gauge Transformations -- 3.1.2 Gauge Potential and Field Strength -- 3.1.3 Field Equations -- 3.1.4 Classical Equations of Motion -- 3.1.5 Duality Symmetry and Beyond -- 3.2 General Relativity -- 3.3 Gravitation and the Gauge Paradigm -- References -- Chapter 4: Fundamentals of Teleparallel Gravity -- 4.1 Some Historical Remarks -- 4.2 Geometrical Setting -- 4.3 Gauge Transformations of Source Fields -- 4.4 Gauge Coupling Prescription -- 4.4.1 The Electromagnetic Case as an Example -- 4.4.2 Translational Coupling Prescription -- 4.4.3 Translational Coupling in a General Frame -- 4.5 Translational Field Strength -- 4.6 Fundamental Fields -- References -- Chapter 5: Gravitational Coupling Prescription -- 5.1 Translational Coupling Revisited -- 5.2 Lorentz Coupling Prescription -- 5.2.1 General Covariance Principle -- 5.2.2 Passage to an Anholonomic Frame -- 5.2.3 Identifying Inertia with Gravitation -- 5.3 Full Gravitational Coupling Prescription -- 5.4 Possible Connections -- References -- Chapter 6: Particle Mechanics -- 6.1 Free Particles Revisited -- 6.1.1 Basic Notions -- 6.1.2 Equation of Motion of Free Particles -- 6.2 Gravitationally Coupled Particles -- 6.2.1 Coupling Prescription. , 6.2.2 Gravitationally Coupled Equation of Motion -- 6.2.3 Equivalence with the Geodesic Equation -- 6.3 Newtonian Limit -- 6.4 Gravitomagnetic Field -- 6.5 Separating Inertial Effects from Gravitation -- 6.6 A Genuine Gravitational Connection -- References -- Chapter 7: Global Formulation for Gravity -- 7.1 Phase Factor Approach -- 7.2 Colella-Overhauser-Werner Experiment -- 7.3 Gravitational Aharonov-Bohm Effect -- 7.4 Quantum Versus Classical Approaches -- References -- Chapter 8: Hodge Dual for Soldered Bundles -- 8.1 Why a New Dual -- 8.2 Dual Torsion -- 8.3 Dual Curvature -- References -- Chapter 9: Lagrangian and Field Equations -- 9.1 Lagrangian of Teleparallel Gravity -- 9.2 Equivalence with Einstein-Hilbert -- 9.3 Matter Energy-Momentum Density -- 9.4 Field Equations -- 9.5 Bianchi Identities -- 9.6 A Glimpse into New General Relativity -- References -- Chapter 10: Gravitational Energy-Momentum Density -- 10.1 Introduction -- 10.2 Field Equations and Conservation Laws -- 10.3 Teleparallel Gravity -- 10.4 General Relativity -- 10.5 Comparison with the Gauge Self-current -- References -- Chapter 11: Gravitation in the Lack of Universality -- 11.1 Gravitation and Universality -- 11.2 The Electromagnetic Coupling Prescription -- 11.3 Gravitation Without Universality -- 11.3.1 Non-universal Coupling Prescription -- 11.3.2 Particle Equation of Motion -- 11.3.3 Global Formulation and the COW Experiment -- 11.4 Non-universality and General Relativity -- References -- Chapter 12: Gravitational Coupling of the Fundamental Fields -- 12.1 Representations of the Lorentz Group -- 12.2 Gravitational Coupling Revisited -- 12.3 Scalar Field -- 12.4 Dirac Spinor Field -- 12.4.1 The Dirac Equation -- 12.4.2 Torsion Decomposition and Spinors -- 12.5 Electromagnetic Field -- References -- Chapter 13: Spin-2 Field Coupled to Gravitation. , 13.1 Conformal Transformations -- 13.2 Fundamental Spin-2 Field -- 13.3 The Flat Spacetime Case -- 13.3.1 Gauge Transformations -- 13.3.2 Field Strength and Bianchi Identity -- 13.3.3 Lagrangian and Field Equation -- 13.3.4 Duality Symmetry -- 13.3.5 Passage to a General Frame -- 13.3.6 Relation to the Metric Approach -- 13.4 Coupling to Gravitation -- 13.4.1 Gravitational Coupling Prescription -- 13.4.2 Field Strength and Bianchi Identity -- 13.4.3 Lagrangian and Field Equation -- 13.5 Spin-2 Field as Source of Gravitation -- 13.6 On Gravitational Waves -- References -- Chapter 14: Teleparallel Equivalent of Some Solutions -- 14.1 de Sitter Spacetime -- 14.1.1 de Sitter Torsion -- 14.1.2 The de Sitter Torsion -- 14.1.3 The de Sitter Force -- 14.2 Teleparallel Equivalent of the Kerr Solution -- 14.2.1 Kerr Torsion -- References -- Chapter 15: Duality Symmetry -- 15.1 Introduction -- 15.2 Duality Symmetry and Gravitation -- 15.3 Linear Gravity -- 15.4 Looking for a Dual Gravity -- 15.5 Some Properties of the Self-dual Gravity -- References -- Chapter 16: Teleparallel Kaluza-Klein Theory -- 16.1 Introduction -- 16.2 Kaluza-Klein Theory: A Brief Review -- 16.3 Five-Vector Potential -- 16.4 Teleparallel Kaluza-Klein -- 16.5 Metric Constraint -- 16.6 Matter Fields -- 16.7 Further Remarks -- References -- Chapter 17: Einstein-Cartan Theory -- 17.1 Introduction -- 17.2 Field Equations -- 17.3 Gravitational Coupling Prescription -- 17.4 Particle Equations of Motion -- 17.5 Some Drawbacks -- References -- Chapter 18: Why to Study Teleparallel Gravity -- 18.1 On the Gravitational Interaction -- 18.2 On Teleparallel Gravity -- 18.2.1 A Gauge Theory for Gravitation -- 18.2.2 Matters of Consistency -- 18.2.3 Gravitational Energy-Momentum Density -- 18.2.4 Coupling of a Fundamental Spin-2 Field to Gravitation -- 18.2.5 Gravitation and Quantum Mechanics. , 18.2.6 Quantizing Gravity -- 18.2.7 A New Insight into Gravity -- References -- Appendix A: The Spinning Particle -- A.1 Action Functional -- A.2 Equations of Motion -- References -- Appendix B: The Connection Space -- B.1 The Space of Lorentz Connections -- B.2 Equivalence Under Contortion Translations -- References -- Appendix C: Teleparallel Field Equation -- C.1 Lagrangian and Field Equation -- C.2 The Superpotential -- C.3 The Energy-Momentum Current -- Appendix D: Dirac Equation -- D.1 Relativistic Fields -- D.2 Dirac Field -- D.3 Covariant Form of the Dirac Equation -- D.4 Spinor Basis and Currents -- References -- Index.