Ramjet and scramjet engines represent a key technology for high-speed airbreathing propulsion due to their ability to operate efficiently at supersonic and hypersonic speeds without requiring rotating parts. A crucial component of these engines is the air intake, which is responsible for compressing the incoming airflow through shock waves before combustion. The design of an efficient intake significantly affects the overall performance of the propulsion system. This thesis focuses on the design, analysis, and optimization of hypersonic intakes, with particular attention to the Busemann intake, which is known for its high efficiency in the inviscid flow regime. The initial phase of this research involves the numerical generation of intake geometries using a MATLAB-based design algorithm.