Since the mid-1970s there has been truly significant advancement in combustion science, spurred by the dual societal concerns for energy sufficiency and environmental quality, and enabled by the rapid increase in the sophistication of mathematical analysis, computational simulation, and experimental techniques. Consequently, we have witnessed the evolvement of combustion from a scientific discipline that was largely empirical to one that is quantitative and predictive, leading to its useful applications in combustion-related engineering devices and practices.

This text reflects my desire to incorporate these advances in my lectures on combustion. As a result, its preparation has been guided by the three distinguishing themes characterizing recent developments in combustion research, namely the canonical formulation of the theoretical foundation; the strong interplay between experiment, theory, and computation; and the description of combustion phenomena from the unified viewpoint of fluid mechanics and chemical kinetics.

The text also emphasizes analytical proficiency by presenting complete, albeit abbreviated, derivations that can be followed by the student with a modest effort. Alternate solutions are sometimes presented to demonstrate that a phenomenon can often be analyzed using different approaches and at different levels of rigor. I hope that through this gentle guidance the student can acquire the needed confidence to tackle more difficult problems on his or her own.

This text grew out of the lecture material prepared for a one-year graduate course that I have given at several academic institutions. No prerequisite in mathematics, fluid mechanics, and chemistry is expected apart from the usual undergraduate education in the physical sciences or mechanical, aerospace, or chemical engineering.