1 The Lorentz Transformation -- 1.1 Inertial Systems -- 1.2 The Principle of Relativity -- 1.3 Consequences from the Principle of Relativity -- Appendix 1: Reciprocity of Velocities -- Appendix 2: Some Orthogonal Concomitants of Vectors -- 1.4 Invariance of the Speed of Light. Lorentz Transformation -- 1.5 The Line Element -- 1.6 Michelson, Lorentz, Poincare, Einstein -- 2 Physical Interpretation -- 2.1 Geometric Representation of Lorentz Transformations -- 2.2 Relativity of Simultaneity. Causality -- 2.3 Faster than Light -- 2.4 Lorentz Contraction -- 2.5 Retardation Effects: Invisibility of Length Contraction and Apparent Superluminal Speeds -- 2.6 Proper Time and Time Dilation -- 2.7 The Clock or Twin Paradox -- 2.8 On the Influence of Acceleration upon Clocks -- 2.9 Addition of Velocities -- 2.10 Thomas Precession -- 2.11 On Clock Synchronization -- 3 Lorentz Group, Poincare Group, and Minkowski Geometry -- 3.1 Lorentz Group and Poincare Group -- 3.2 Minkowski Space. Four-Vectors -- 3.3 Passive and Active Transformations. Reversals -- 3.4 Contravariant and Covariant Components. Fields -- 4 Relativistic Mechanics -- 4.1 Kinematics -- Appendix: Geometry of Relativistic Velocity Space -- 4.2 Collision Laws. Relativistic Mass Increase -- 4.3 Photons: Doppler Effect and Compton Effect -- 4.4 Conversion of Mass into Energy. Mass Defect -- 4.5 Relativistic Phase Space -- Appendix: Invariance of Rn(q) -- 5 Relativistic Electrodynamics -- 5.1 Forces -- 5.2 Covariant Maxwell Equations -- 5.3 Lorentz Force -- 5.4 Tensor Algebra -- 5.5 Invariant Tensors, Metric Tensor -- 5.6 Tensor Fields and Tensor Analysis -- 5.7 The Full System of Maxwell Equations. Charge Conservation -- 5.8 Discussion of the Transformation Properties -- 5.9 Conservation Laws. Stress-Energy-Momentum Tensor -- 5.10 Charged Particles -- 6 The Lorentz Group and Some of Its Representations -- 6.1 The Lorentz Group as a Lie Group -- 6.2 The Lorentz Group as a Quasidirect Product -- 6.3 Some Subgroups of the Lorentz Group -- Appendix 1: Active Lorentz Transformations -- Appendix 2: Simplicity of the Lorentz Group L++ -- 6.4 Some Representations of the Lorentz Group -- 6.5 Direct Sums and Irreducible Representations -- 6.6 Schur's Lemma -- 7 Representation Theory of the Rotation Group -- 7.1 The Rotation Group SO(3,R) -- 7.2 Infinitesimal Transformations -- 7.3 Lie Algebra and Representations of SO(3) -- 7.4 Lie Algebras of Lie Groups -- 7.5 Unitary Irreducible Representations of SO(3) -- 7.6 SU(2), Spinors, and Representation of Finite Rotations -- 7.7 Representations on Function Spaces -- 7.8 Description of Particles with Spin -- 7.9 The Full Orthogonal Group 0(3) -- 7.10 On Multivalued and Ray Representations -- 8 Representation Theory of the Lorentz Group -- 8.1 Lie Algebra and Representations of L++ -- 8.2 The Spinor Representation -- 8.3 Spinor Algebra -- Appendix: Determination of the Lower Clebsch-Gordan Terms -- 8.4 The Relation between Spinors and Tensors -- Appendix 1: Spinors and Lightlike 4-Vectors -- Appendix 2: Intrinsic Classification of Lorentz Transformations -- 8.5 Representations of the Full Lorentz Group -- 9 Representation Theory of the Poincaré Group -- 9.1 Fields and Field Equations. Dirac Equation -- Appendix: Dirac Spinors and Clifford-Dirac Algebra -- 9.2 Relativistic Covariance in Quantum Mechanics -- 9.3 Lie Algebra and Invariants of the Poincare Group -- 9.4 Irreducible Unitary Representations of the Poincare Group -- 9.5 Representation Theory of P++ and Local Field Equations -- 9.6 Irreducible Semiunitary Ray Representations of P -- 10 Conservation Laws in Relativistic Field Theory -- 10.1 Action Principle and Noether's Theorem -- 10.2 Application to Poincaré-Covariant Field Theory -- 10.3 Relativistic Hydrodynamics -- Appendices -- A Basic Concepts from Group Theory -- A.1 Definition of Groups -- A.2 Subgroups and Factor Groups -- A.3 Homomorphisms, Extensions, Products -- A.4 Transformation Groups -- B Abstract Multilinear Algebra -- B.1 Semilinear Maps -- B.2 Dual Space -- B.3 Complex-Conjugate Space -- B.4 Transposition, Complex, and Hermitian Conjugation -- B.5 Bi- and Sesquilinear Forms -- B.6 Real and Complex Structures -- B.7 Direct Sums -- B.8 Tensor Products -- B.9 Complexification -- B.10 The Tensor Algebra over a Vector Space -- B.11 Symmetric and Exterior Algebra -- B.12 Inner Product. Creation and Annihilation Operators -- B.13 Duality in Exterior Algebra -- C Majorana Spinors, Charge Conjugation, and Time Reversal in Dirac Theory -- C.1 Dirac Algebra Reconsidered -- C.2 Majorana Spinors, Charge Conjugation, Time Reversal -- D Poincaré Covariance in Second Quantization -- D.l The One-Particle Space -- D.2 Fock Space and Field Operator -- D.3 Poincaré Covariance and Conserved Quantities -- Notation -- Author Index.