We study some deterministic Mean Field Games problems with finite horizon where the players are constrained to remain in a network. Here, a network is given by a finite collection of vertices connected by continuous edges which cannot self-intersect. The generic player controls instantaneously its velocity, and when it occupies a vertex, it can enter into any incident edge. The running and terminal costs depends on the global distribution of the players and are assumed to be continuous inside each edge but not necessarily globally continuous on the network. Moreover, the running cost has a not-separated structure, namely it does not depends separately from the control and from space-time. We first study the optimal control problem associated to such Mean Field Games and we prove the existence of optimal trajectories and their Lipschitz continuity, some regularity properties of the value function inside the edges and a closed graph property for the map which associates to each point of the network the set of optimal trajectories starting from that point. Afterwards, we tackle the Mean Field Games following a Lagrangian approach. We obtain the existence of relaxed equilibria consisting of probability measures on admissible trajectories. To any relaxed equilibrium corresponds a mild solution, i.e. a pair $(u, m)$ made of the value function $u$ of a related optimal control problem and a family $m = (m(t))_t$ of probability measures on the network. Given $m$, the value function $u$ is a viscosity solution of a Hamilton-Jacobi problem on the network. We then investigate a weak form of a Fokker-Planck equation satisfied by $m$. This is a joint work with Y. Achdou, P. Mannucci and N. Tchou.