1. Introduction and overview of supersonic and hypersonic flows 2. Fundamentals of boundary layer instability theory and transition mechanisms 3. Multi-dimensional stability analysis of supersonic and hypersonic boundary layers 4. Receptivity of hypersonic boundary layers 5. Parabolized stability equations for hypersonic boundary layers 6. Breakdown to turbulence and DNS of hypersonic boundary layers 7. Transient growth and input/output analysis 8. Isotropic turbulence and its interaction with shock waves 9. Compressible turbulent shear layers 10. Wall-bounded compressible turbulent flows 11. Shock-wave/boundary-layer interactions 12. Jet noise 13. Turbulence modelling in compressible flows