1. A brief review of general relativity
2. A kinetic-theory description of fluids
3. Relativistic perfect fluids
4. Linear and nonlinear hydrodynamic waves
5. Reaction fronts: detonations and deflagrations
6. Relativistic non-perfect fluids
7. Formulations of the Einstein-Euler equations
8. Numerical relativistic hydrodynamics: finite-difference methods
9. Numerical relativistic hydrodynamics: HRSC methods
10. Numerical relativistic hydrodynamics: high-order methods
11. Relativistic hydrodynamics of non-selfgravitating fluids
12. Relativistic hydrodynamics of selfgravitating fluids
Appendix A. Geometrised system of units
Appendix B. Notable thermodynamic expressions
Appendix C. Notable tensors
Appendix D. Common practices in numerical relativistic hydrodynamics
Appendix E. Numerical building blocks

This title provides an up-to-date, lively and approachable introduction to the mathematical formalism, numerical techniques and applications of relativistic hydrodynamics. The topic is presented here in a form which will be appreciated both by students and researchers in the field.