The study of boundary layer flows of non-Newtonian fluids is an important and challenging task in fluid mechanics. The recent decades saw a lot of interest in this area because of the fact that many important industrial fluids are non-Newtonian in their flow characteristics. The main aim of this thesis is to explore and analyze the boundary layer flow with heat transfer of a non-Newtonian fluid. Thus, this thesis revolves around one of the paramount subclass of non-Newtonian fluids namely the modified second grade fluid (MSGF). Despite of the diverse applicability of this fluid model in technological fields, not much study has been made on flow and heat transfer characteristics of MSGF. In view of this, the research presented in this thesis is carried out to fill up the existing gap in literature. Boundary layer equations for the flow and heat transfer of modified second grade fluid are bestowed in Cartesian as well as cylindrical polar coordinates. Additionally, the non-linear stretching surfaces are investigated keeping in view different geometries like stretching cylinder, radially stretching sheet and planar stretching sheet. Numerous effects of flow and heat transfer are incorporated namely the stagnation point flow, magnetohydrodynamic (MHD) flow, nanoparticles, mixed convection heat transfer, linear and non-linear thermal radiation, homogeneous-heterogeneous reactions, Newtonian heating and convective boundary conditions. The governing problems comprising of highly non-linear partial differential equations are simplified by suitable transformations into the corresponding ordinary differential equations. The resultant systems of equations are numerically handled by the Runge-Kutta Fehlberg scheme and bvp4c in MATLAB. The legitimacy of the numerical results is ensured by presenting a comparative study for special cases. The graphical and tabular illustrations are displayed for various pertinent parameters to obtain the physical insight of the problem. In addition, exact solutions are also calculated for few problems by considering special cases. One of the key observation is that the generalized second grade parameter strengthens the fluid velocity while diminishes the temperature of the fluid.