In this report it is investigated if the Manifold Mapping method can be used in airfoil optimization. Before the method can be implemented, a suitable airfoil parametrization must be chosen. Furthermore a coarse and fine model must be assigned. These models are the key to success for the Manifold Mapping method. If two models are chosen that are completely different from each other, the Manifold Mapping will not work properly. Furthermore, if two models are chosen that are very similar to each other, the benefit in reducing computational cost will be only marginal. In this report the Manifold Mapping method will be explained in detail and applied to airfoil design. The approach is validated by using a test case, which will also be explained in detail. Furthermore recommendations and extensions will be given in the last chapter
