Combustion is an old technology, which at present provides about 90% of our worldwide energy support. Combustion research in the past used fluid mechanics with global heat release by chemical reactions described with thermodynamics, assuming infinitely fast reactions. This approach was useful for stationary combustion processes, but it is not sufficient for transient processes like ignition and quenching or for pollutant formation. Yet pollutant formation during combustion of fossil fuels is a central topic and will continue to be so in the future. This book provides a detailed and rigorous treatment of the coupling of chemical reactions and fluid flow. Also, combustion-specific topics of chemistry and fluid mechanics are considered and tools described for the simulation of combustion processes. The actual fourth edition presents a completely restructured book: Mathematical Formulae and derivations as well as the space-consuming reaction mechanisms have been replaced from the text to appendix. A new chapter discusses the impact of combustion processes on the earths atmosphere, the chapter on auto-ignition is extended to combustion in Otto- and Diesel-engines, and the chapters on heterogeneous combustion and on soot formation appear heavily revised.