This book deals with applications of symmetry groups to solve physically important Einstein field equations, which are-the nondiagonal Einstein-Rosen metrics, the Einstein-Maxwell equations, Einstein-Maxwell equations for the magnetostatic fields, the Einstein-Maxwell equations for non-static Einstein and Rosen metrics, Einstein Vacuum equations for axially symmetric gravitational fields. To solve these highly nonlinear systems of partial differential equations (PDEs), Lie Classical method, symmetry reduction method and (G'/G)-expansion method are utilized. Symmetries are derived to reduce these systems of PDEs to ODEs and some exact solutions are obtained. Some of these solutions are also represented graphically.