Vehicle Energy and Fuel Consumption — Basic Concepts -- IC-Engine-Based Propulsion Systems -- Models of Electric and Hybrid-Electric Propulsion Systems -- Models of Hybrid-Inertial and Hybrid-Hydraulic Propulsion Systems -- Models of Fuel-Cell Propulsion Systems -- Supervisory Control Algorithms -- Appendix I — Case Studies -- Appendix II — Optimal Control Theory.Automobiles are responsible for a substantial part of the world's consumption of primary energy, mostly fossil liquid hydrocarbons. The reduction of the fuel consumption of these vehicles has become a top priority. Many ideas to reach that objective have been presented. In most cases these systems are more complex than the traditional approaches. For such complex systems a heuristic design approach fails. The only way to deal with this situation is to employ model-based methods. This text provides an introduction to the mathematical modeling and subsequent optimization of vehicle propulsion systems and their supervisory control algorithms.