The theory of mean-field games comprises a set of tools and methods, that aims at investigating differential games involving a (very) large number of rational, indistinguishable players. These were introduced in the independent works of Lasry and Lions [37–40] and Huang et al.[34, 35]. Since then, there has been intense research activity in this field, with several authors considering a variety of related problems. These include numerical methods [2, 3, 36], applications in economics [32, 41] and environmental policy [36], finite state problems [17, 27, 28], explicit models [33, 45], obstacle-type problems [19], congestion [18, 25], extended mean-field games [24, 29], probabilistic methods [13, 14], long-time behavior [8, 11] and weak solutions [9, 47, 48], to name only a few. For additional results, see also recent surveys in [1, 7, 42], or [23] and the references therein, and the College de France lectures by Lions [43, 44].