This thesis explores the formulation, derivation, and implementation of the continuous adjoint equations for hypersonic, nonequilibrium flow environments. The adjoint method is an efficient means for acquiring sensitivity information that can be used in a gradient-based framework to perform optimal shape design of aerospace systems. A solution to the adjoint system of equations carries a computational cost roughly equal to a single solution of the flow governing equations, regardless of the dimensionality of the design space. When compared to other gradient acquisition methods, where computational costs scale with design space dimensionality, the adjoint method is superior when the dimensionality is high and when solutions to the governing equations are expensive. Such conditions are often representative of most aerospace problems of practical interest. In addition to providing gradient information, solutions to the adjoint equations may be used assensors' orweighting factors' to perform error estimation and adaptive mesh refinement.