Differential geometry of translation surfaces

This thesis consists of four chapters.In the first chapter, the basic definitions and theorems are given related to this subject.In the second chapter, differential geometric properties of translation surfaces in 3-dimensional Euclidean space are given. Hence, shape operator matrix along generator curves of surface, Gaussian curvature, mean curvature, curvatures along generator curves of surface, fundemantel forms of surface, principal lines and lines of principal curvature, umbilic points, asimptotic lines and geodesics are given.In the third chapter, minimal translation surfaces and differential geometric properties are given.In the fourth chapter, differential geometric properties of surfaces that are parallel to translation surfaces in 3-dimensional Euclidean space which are constructed by generator curves with constant curvatures and torsions are given.