Book excerpt: The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications. The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss. Contents: On Whitham Equations for Camassa-Holm (S Abenda et al.); An Operational Description of Stock Markets (F Bagarello); Vortex Layers in the Small Viscosity Limit (R E Caflisch & M Sammartino); Integration of Partially Integrable Equations (R Conte); Waves and Vibrations in a Solid of Second Grade (M Destrade & G Saccomandi); Multicomponent Reactive Flows (V Giovangigli); Singularities for Prandtl''s Equations (G Lo Bosco et al.); Stability of Solitons of the ZakharovOCoRubenchik Equation (F Oliveira); Plain Waves and Vibrations in the Elastic Mixtures (M Svanadze); Extended Thermodynamics with Consistent Order (W Weiss); and other papers. Readership: Academics, researchers and post-graduates in mathematics and physics."