This second edition with four additional chapters presents the physical principles and solution techniques for transient propagation in fluid mechanics and hydraulics. The application domains vary including contaminant transport with or without sorption, the motion of immiscible hydrocarbons in aquifers, pipe transients, open channel and shallow water flow, and compressible gas dynamics. The mathematical formulation is covered from the angle of conservation laws, with an emphasis on multidimensional problems and discontinuous flows, such as steep fronts and shock waves. Finite difference-, finite volume- and finite element-based numerical methods (including discontinuous Galerkin techniques) are covered and applied to various physical fields. Additional chapters include the treatment of geometric source terms, as well as direct and adjoint sensitivity modeling for hyperbolic conservation laws. A concluding chapter is devoted to practical recommendations to the modeler. Application exercises with on-line solutions are proposed at the end of the chapters.