This course provides the students who are intending a career in combustion/reacting flows, fluid mechanics or propulsion an opportunity to do an in-depth study of some of the current academic research areas with implications of practical importance. It will also be suitable for graduate students who have a good background in essentials of their research area, but need a specialized course to cover material not available in other graduate courses. The intention is not to replace or to overlap with the literature review of the students theses work. The course will cover 3 to 4 topics from the following: non-intrusive experimental; techniques in isothermal and reacting flows; activation energy asymptotics; high-speed combustion; metal combustion in propulsion; thermo-acoustics in propulsion systems; soot formation and oxidation kinetics; theory of partially premixed turbulent combustion; synthesis of nano-materials by combustionhigh-pressure combustion. Topic selection will depend on the interests of the students taking the course. Similar topics will be added as needed.