The work considers some free surface problems and attempts to understand the intrinsic complex behavior of waves in thin films down an inclined plane or vertical wall. The viscous Newtonian thin film or non-Newtonian inelastic power-law film or viscoelastic film down an inclined plane or vertical wall is considered and dynamics of waves and stability characteristics of thin film flow systems are analyzed. The investigations are based on the derivation of an amplitude equation of Landau-Stuart type for the evolution of waves for isothermal or non-isothermal films valid in the neighborhood of a neutral curve or on the use of modern bifurcation techniques of dynamical systems theory together with direct numerical integration to construct weakly nonlinear permanent waves on Newtonian / viscoelastic films for moderate to high Reynolds numbers and small to moderate surface tension effects. The work also considers the development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field with or without induced air shear effects. The entire work is divided into seven chapters.