Foreword. 1 The De Giorgi Method for Nonlocal Fluid Dynamics -- 2 Recent Results on the Periodic Lorentz Gas -- 3 The Boltzmann Equation in Bounded Domains -- 4 The Concentration-Compactness/Rigidity Method for Critical Dispersive and Wave Equations.

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 Schrödinger and wave equations. Several powerful methods from recent top research articles are described in a careful and expository manner.