In this thesis that is based on [?, ?, ??, ??], we use some spaces such as Euclidean space, Lorenz-Minkowski space, simply isotropic space and Galilean space to prove some theorems depend on translation surfaces in mentioned spaces. The tools of this study are first, second and third fundamental form. We recall that the mentioned spaces have three dimentional real space as ambient space, but each of them has its own metric.
