The contributions to the book concern various aspects of extension of classical continuum models. These extensions are related to the appearance of microstructures both natural as well as these created by processes. To the first class belong various thermodynamic models of multicomponent systems such as porous materials, composites, materials with microscopic heterogeneities. To the second class belong primarily microstructures created by phase transformations. Invited authors cover both fields of thermodynamic modeling and mathematical analysis of such continua with microstructure. In particular the following subjects are covered: • thermodynamic modeling of saturated and unsaturated porous and granular media, • linear and nonlinear waves in such materials, • extensions of constitutive laws by internal variables, higher gradients and nonequilibrium fields, • shastic processes in porous and fractal materials, • thermodynamic modeling of composite materials, • mathematical analysis of multicomponent systems, • phase transformations in solids.