A brief account of research activities on problems related to air-breathing propulsion is made in this final report for the step funded research grant NASA NGL 14-005-140. Problems include the aircraft ejector-nozzle propulsive system, nonconstant pressure jet mixing process, recompression and reattachment of turbulent free shear layer, supersonic turbulent base pressure, low speed separated flows, transonic boattail flow with and without small angle of attack, transonic base pressures, Mach reflection of shocks, and numerical solution of potential equation through hodograph transformation.