This thesis presents a shape optimization framework for problems that are encountered routinely in Aerodynamic Design. The nature of the framework is numerical. Its focus is wide as different aspects of the shape optimization practice are treated, e.g., the solution of the flow equations, the sensitivity analysis and the parameterization of the shape. The framework components are not taken as black-boxes but are conceived and implemented within the present work. A considerable part of the thesis describes the characteristics and the implementation of those components. Additional work on unsteady flows, which may find applications in aeroelastic analysis, is presented in the appendix.