“This book deals with the Riemann problem in continuum physics in a clear, rigorous and complete way. ... This monograph constitutes a very useful starting point for a non-expert scholar who finds in a single updated work both the theoretical and the applied aspects. At the same time, however, the book is also of great value for expert researchers.” (Francesca Brini, Mathematical Reviews, May, 2025)

• 1 Overview of this monograph.- 2 Models arising in fluid and solid dynamics.- 3 Nonlinear hyperbolic systems of balance laws.- 4 Riemann problem for ideal fluids.- 5 Compressible fluids governed by a general equation of state.- 6 Nonclassical Riemann solver with prescribed kinetics. The hyperbolic regime.- 7 Nonclassical Riemann solver with prescribed kinetics. The hyperbolic-elliptic regime.- 8 Compressible fluids in a nozzle with discontinuous cross-section. Isentropic flows.- 9 Compressible fluids in a nozzle with discontinuous cross-section. General flows.- 10 Shallow water flows with discontinuous topography.- 11 Shallow water flows with temperature gradient.- 12 Baer-Nunziato model of two-phase flows.- References.- Index.