**1. Fundamentals of Special Relativity**

Introduction

The Principle of Relativity

Groups—the Galilei group

Galileian law of addition of velocities

The lesson from electromagnetism

The postulates of Special Relativity

Consequences of the postulates

Conclusion

Problems

**2. The Lorentz transformation**

Introduction

The Lorentz transformation

Derivation of the Lorentz transformation

Mathematical properties of the Lorentz transformation

Absolute speed limit and causality

Length contraction from the Lorentz transformation

Time dilation from the Lorentz transformation

Transformation of velocities and accelerations in Special Relativity

Matrix representation of the Lorentz transformation

The Lorentz group

The Lorentz transformation as a rotation by an imaginary angle with imaginary time

The GPS system

Conclusion

Problems

**3, The 4-dimensional world view**

Introduction

The 4-dimensional world

Spacetime diagrams

Conclusion

Problems

**4. The formalism of tensors**

Introduction

Vectors and tensors

Contravariant and covariant vectors

Contravariant and covariant tensors

Tensor algebra

Tensor fields

Index-free description of tensors

The metric tensor

The Levi-Civita symbol and tensor densities

Conclusion

Problems

**5. Tensors in Minkowski spacetime**

Introduction

Vectors and tensors in Minkowski spacetime

The Minkowski metric

Scalar product and length of a vector in Minkowski spacetime

Raising and lowering tensor indices

Causal nature of 4-vectors

Hypersurfaces

Gauss’ theorem

Conclusion

Problems

**6. Relativistic mechanics**

Introduction

Relativistic dynamics of massive particles

The relativistic force

Angular momentum of a particle

Particle systems

Conservation of mass-energy

Conclusion

Problems

**7. Relativistic optics**

Introduction

Relativistic optics: null rays

The drag effect

The Doppler effect

Aberration

Relativistic beaming

Visual appearance of extended objects

Conclusion

Problems

**8. Measurements in Minkowski spacetime**

Introduction

Energy of a particle measured by an observer

Frequency measured by an observer

A more systematic treatment of measurement

The 3+1 splitting

Conclusion

Problems

**9. Matter in Minkowski spacetime**

Introduction

The energy-momentum tensor

Covariant conservation

Energy conditions

Angular momentum

Perfect fluids

The scalar field

The electromagnetic field

Conclusion

Problems

**10. Special Relativity in arbitrary coordinates**

Introduction

The covariant derivative

Spacetime curves and covariant derivative

Physics in Minkowski spacetime revisited

Conclusions

Problems

Solutions to selected problems

References

Index