This paper presents a macroscopic multi-class traffic flow model on road networks that accounts for an arbitrary number of vehicle classes with different free flow speeds. A comparison of the Eulerian and Lagrangian formulations is proposed, with the introduction of a new Courant-Friedrichs-Lewy condition. In particular, the L 1-error and the computational times are used to compare the performance of the two formulations and show that the Eulerian formulation outperforms the Lagrangian. The paper then extends the Eulerian formulation to traffic networks, providing a general implementation of the dynamics at junctions. We finally simulate the effect of traffic measures and policies, such as route guidance and modal shift, on total travel time and network throughput, which shows that the proposed multi-class model correctly depicts the interactions among classes and it can be used to model such behaviors in complex networks.