This paper introduces the adjoint approach to design, focusing on its application in computational fluid dynamics (CFD), particularly for aeronautical applications. It emphasizes the simplicity of adjoint methods in the context of linear algebra and extends the discussion to partial differential equations (PDEs). The paper discusses the construction of the adjoint PDE, its boundary conditions, and the physical significance of the adjoint solution. It concludes with examples of adjoint methods used to optimize the design of business jets. Adjoint equations have a long history in optimal control theory. In fluid dynamics, Pironneau first used adjoint equations for design, while Jameson pioneered their use in aeronautical CFD. He developed adjoint approaches for potential flow, Euler equations, and Navier-Stokes equations, progressing from 2D airfoil optimization to 3D wing design and complete aircraft configurations. Several research groups have developed adjoint CFD codes for design optimization. Elliott and Anderson worked on unstructured grids using the 'discrete' adjoint approach, while Mohammadi used automatic differentiation software to generate adjoint codes from original CFD codes. These approaches are discussed in the paper. Despite the importance of design in aeronautical engineering, the development of adjoint CFD codes has not been rapid since Jameson's first papers. This may be due to the complexity of the adjoint approach, both in mathematical formulation and in code creation. The paper addresses these difficulties by first presenting adjoint theory in the context of linear algebra, which is the basis for the discrete adjoint CFD approach. It then discusses the extension to PDEs, focusing on the construction of the adjoint PDE, its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with a discussion of the pros and cons of discrete and continuous approaches, and examples of adjoint methods used to optimize business jet designs.This paper introduces the adjoint approach to design, focusing on its application in computational fluid dynamics (CFD), particularly for aeronautical applications. It emphasizes the simplicity of adjoint methods in the context of linear algebra and extends the discussion to partial differential equations (PDEs). The paper discusses the construction of the adjoint PDE, its boundary conditions, and the physical significance of the adjoint solution. It concludes with examples of adjoint methods used to optimize the design of business jets. Adjoint equations have a long history in optimal control theory. In fluid dynamics, Pironneau first used adjoint equations for design, while Jameson pioneered their use in aeronautical CFD. He developed adjoint approaches for potential flow, Euler equations, and Navier-Stokes equations, progressing from 2D airfoil optimization to 3D wing design and complete aircraft configurations. Several research groups have developed adjoint CFD codes for design optimization. Elliott and Anderson worked on unstructured grids using the 'discrete' adjoint approach, while Mohammadi used automatic differentiation software to generate adjoint codes from original CFD codes. These approaches are discussed in the paper. Despite the importance of design in aeronautical engineering, the development of adjoint CFD codes has not been rapid since Jameson's first papers. This may be due to the complexity of the adjoint approach, both in mathematical formulation and in code creation. The paper addresses these difficulties by first presenting adjoint theory in the context of linear algebra, which is the basis for the discrete adjoint CFD approach. It then discusses the extension to PDEs, focusing on the construction of the adjoint PDE, its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with a discussion of the pros and cons of discrete and continuous approaches, and examples of adjoint methods used to optimize business jet designs.