Explore the mathematical foundations and computational approaches to Mean-Field Games (MFGs) through this 38-minute conference talk that examines Nash equilibrium in non-cooperative games with a continuum of players. Discover the broad applications and deep connections MFGs have to sampling, optimal transport, and economics while gaining insights through numerical analysis and computational methods. Learn about convergence analysis of learning algorithms for MFGs, understanding how the best response plays a central role in both game dynamics and algorithm behavior. Examine an iterative strategy for solving inverse MFG problems, revealing how measurements of Nash equilibrium states can effectively infer unknown ambient potentials such as obstacles. Gain understanding of both forward and inverse problems in MFGs through research findings that bridge theoretical analysis with practical computational solutions.