The analysis and model ing of large-scale systems , due to a variety of applications that is emerging for them , are getting more and more importance these days . In such systems , as we face large numbers of players that have interdependence with each other , analysis the system and finding equilibrium points with common mathematical tools lead to technical problems both analytically and numerically . The Mean Field Games approach enables us to formulate our large-scale problem in a framework that enables us to speak about the existence of such equilibrium points and also provides us with ways to find them . One of the prominent and fast growing applications of such large-scale systems is the problem of designing a charging policy for large numbers of electric vehicles . The significant market penetration of electric vehicles over the next few years could have potential impacts on the power grid . For example the simultaneous charging of electric vehicles could lead to new peaks in the energy profile . Now the question is that how one could regulate the collective electric vehicles charging profile in a way to reduce these side effects . Both centralized and decentralized approaches have been proposed in the literature . Clearly , from the energy operator point of view , centralized approaches are preferable . However , as these approaches do not pay enough attention to users' privacy and goals , therefore they face applicability difficulties . Moreover , the increase in the number of electric vehicles , confronts centralized approaches with computational problems . Therefore , the mean field games approach introduces a decentralized framework that enables us to consider both system level concerns and individual electric vehicle goals and at the same has the ability to track the problem and speak about the existence and uniqueness of equilibrium points and calculates them . In this thesis , first we introduce mean field games and provide algorithms to calculate their Nash equilibrium . Then we move forward to introduce decentralized approaches in charging large number of electric vehicles using ideas from mean field games theory . Also we focus on the strength of the mean field games approach on handling problems with stochastic dynamical equations and complicated cost functions for electric vehicles . Key Words: Mean Field Games Theory , - Nash Equilibrium , Decentralized Control , Electric Vehicles , Hamilton-Jacobi-Bellman Equation , Fokker-Planck-Kolmogorov Equation