In this thesis, we propose a new class of inverse problems to recover Lagrangians in MeanField Games from boundary data. We present strategies to address these problems when the Lagrangian we are searching for is assumed to be analytic. Our study can be viewed as an extension of inverse problems from Riemannian manifolds to infinite-dimensional metric spaces, such as the Wasserstein space, which possess differential structures. It can also be regarded as an infinite-dimensional version of the travel time tomography problem. The application of our inverse problem is to learn the rules governing people’s migration when we have limited knowledge of their movements at the boundary.