Main subject categories: • Stationary partial differential equations • Differential equations • Partial differential equations • Evolutionary Partial differential equations • Gradient flows of probability measures • The mathematics of chemotaxis • Examples of singular limits in hydrodynamics • Notes on hyperbolic systems of conservation laws and transport equations • Collisionless kinetic equations from astrophysics ‒ the Vlasov-Poisson system • Soner: Stochastic representations for non-linear parabolic PDE's • Controllability and observability of partial differential equations: Some results and open problemsThe original aim of this series ofHandbook of Differential Equationswas to acquaint the interested reader with the current status of the theory of evolutionary partial differential equations, with regard to some of its applications in physics, biology, chemistry, economy, among others. The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of nonlinear parabolic PDEs.The aim here is to collect review articles, written by leading experts, which will highlight the present as well as expected future directions of development of the field with particular emphasis on applications.