The classification of combustion phenomena into premixed and non-premixed combustion is used throughout this course. After an introduction into the basic thermodynamics in Lecture 1, chemical kinetics in Lecture 2 and 3, ignition and extinction phenomena.in Lecture 4 and the balance equations of fluid dynamics in Lecture 5 laminar premixed flames are treated in Lecture 68 and laminar diffusion flames in Lectures 9 and 10. Then an introduction into turbulent combustion is given in Lecture 11. Non-premixed turbulent combustion is presented in Lectures 12 and 13 while premixed turbulent combustion is treated in Lecture 14. Finally, a Lecture on partially premixed turbulent combustion closes the course.