This book provides a lively and approachable introduction to the main concepts and techniques of relativistic hydrodynamics in a form that will appeal to physicists at advanced undergraduate and post-graduate levels. The book is divided in three parts. The first part deals with the physical aspects of relativistic hydrodynamics, touching fundamental topics such as kinetic theory, equations of state, linear and nonlinear waves in fluids, and the treatment ofnon-ideal fluids. The second part provides an introductory but complete description of those numerical methods currently adopted in the solution of the relativistic hydrodynamic equations. Finally, the thirdpart is devoted to applications and considers several physical and astrophysical systems for which relativistic hydrodynamics plays a crucial role. The book is especially recommended to astrophysicists, particle physicists, and applied mathematicians.