Impulsive hybrid discrete-continuous delay differential equations. This thesis deals with impulsive hybrid discrete-continuous delay differential equations (IHDDEs). This new class of differential equations is highly challenging for two reasons. First, because of a dependency of the right-hand-side function on past states, with time delays that depend on the current state. Second, because both the right-hand-side function and the state itself are discontinuous at implicitly defined time points. ... The practical implementation of all developed methods in the new software packages Colsol-DDE and ParamEDE is described.