The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schroedinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles. 10 Illustrations, color; 23 Illustrations, black and white; VIII, 150 p. 33 illus., 10 illus. in color.