This thesis demonstrates the existence of simple representations in any dimension of a specific collection of Baumslag-Solitar groups, BS (m, n), and investigates their deformations. Specifically, the dimension of the tangent space of the representation scheme of this collection of groups, at these specific representations, is computed. Moreover, we then deduce the dimension of the representation scheme itself. We also investigate the geometry of the character variety of the group in a neighborhood of these special representations.