Daily traffic patterns are the result of a large number of individual decisions, where each driver chooses an optimal departure time and an optimal route to reach destination.    The first part of the talk will review some mathematical models of traffic flow on a network of roads.Along each road, the density of cars is described by a scalar conservation law.These PDEs are then supplemented by suitable boundary conditions at junctions.To study drivers'  behavior, one can then introduce a cost functional, accounting for thetime that each driver spends on the road and a penalty for late arrival.Assuming some simple boundary conditions at intersections,by topological techniques one proves the  existence of a Nash equilibrium,where no driver can lower his own cost by choosing a different departure time ora different route to reach destination.    The existence of an equilibrium  is still an open question in the case of more general (and realistic) conditions at road intersections.Another  intriguing mathematical problem is  the dynamic stability ofNash equilibria.    In this direction, some numerical experiments and conjectures will be discussed.