Diogo Aguiar Gomes King Abdullah Univ. of Science and Technology (KAUST) In this talk, we explore a number of techniques from monotone operator theory in the study of stationary and time-dependent mean-field games. First, we use the monotone operator framework to establish the existence of weak solutions for stationary problems both in the periodic setting and with boundary conditions. Then, we examine applications to numerical methods, both for stationary problems and problems with boundary conditions.