Embedded computer systems are in constant interaction with their environment, which often contains continuous-state and continuous-time components. This results in complex interactions between discrete calculation and decision-making processes on the one hand and continuous processes on the other, which cannot be analysed using either continuous or discrete mathematics. In this respect, an independent theory and design methodology is required to analyse this technically important class of computer-based systems, which this lecture aims to introduce: the theory of hybrid discrete-continuous systems. The lecture will be accompanied by a semester project using current design and verification tools to consolidate the lecture material.