Differential game theory is a branch of mathematics that touches many fields such as control and game theories, probability, stochastic and partial differential equations. An interesting aspect of it is studying strategies of the players which are optimal in that they produce a situation of equilibrium, for example in the famous sense due to Nash, and also seeing what happens when the number of players grows and possibly becomes infinite. 

In this talk I will try to give a brief introduction to this theory aimed at a wide audience of mathematicians possibly unaware of the subject, with the final purpose of presenting the main topics which my doctoral research focused on.