Abstarct: In this thesis in the first chapter we give the basic concepts of Finsler geometry. Then, we consider Randers metrics as a special case of Finsler metrics, and study some geometrical properties of these metrics. Projectively flat Randers metrics with isotropic S-curvature are considered and the classification theorem of this type of metrics is presented. Finally, we give the classification theorem of Randers metrics of scalar flag curvature with isotropic S-curvature.