The annual lecture series in computational fluid dynamics brings in-depth presentations on well-established and recent advances in the field of algorithm development for numerical flow simulation. This year?s edition will focus on novel methods for solving hyperbolic, or more generally, dispersion-dominated systems. The numerical approaches that will be covered are (1) discontinuous Galerkin methods generalizing classical finite volume approaches and (2) residual distributive methods which have been proposed over recent years as an alternative for stabilized least squares Galerkin finite element methods. A posteriori error estimators related to these methods will also be discussed in detail. Applications will be shown in compressible transonic and supersonic aerodynamics, ideal MHD and two-fluid two-phase flow problems.