In this thesis, we study the stability and stabilization of some distributed pa rameters systems, namely, heat and wave equations. First, we investigate the sta bility of one-dimensional heat systems using frequency (eigenvalues) and energy (norm) methods. Then, we use the back-stepping method to stabilize unstable heat equations with different boundary feedback controls. Next, we investigate the stability of a one-dimensional wave equation with some specific boundary conditions. Finally, we propose interior feedback control and boundary feedback 0 CY control in order to improve the stability of such systems. The proof is based on the energy method.