Coupled problems often comprise lumped elements, which are described by pure topological quantities, and distributed elements with space dimension of one to three. Modelling these systems yields partial differential-algebraic systems, for short PDAEs, which link differential-algebraic (DAE) models for lumped elements with PDE models for distributed ones. DAE and PDE models are linked by source terms and boundary conditions. The block course will analyse PDAE models from a modelling perspective based on applications from different fields, an analytic perspective (well-posedness, sensitivity and property preservation), as well as a numerical perspective (co-simulation and dynamic iteration, multirate and MOR schemes). The course will combine theoretical lectures with hands-on experiences gained by lab exercises.