This thesis presents a theoretical discussion of the full evolution of Supernova Remnants (SNRs), that includes the thermalization of the SN ejecta, the Sedov-Taylor and Snowplough stages of the SNR evolution. Our aim is to study how such evolution proceeds for different values of the ambient gas density. A fast numerical method based on the Thin-Shell approximation is developed. The ejecta density and velocity configurations are included in order to study the ejecta-dominated (ED) or thermalization phase, and the transition to the Sedov-Taylor (ST) stage. The numerical scheme also includes radiative cooling. The calculations show that for low-density models, the remnants follow the classical evolutionary tracks with a negligible amount of energy radiated from the shocked ejecta gas and are in excellent agreement with the literature. For high-density models, strong radiative cooling, both from the shocked ejecta and shocked ambient gas, leads the SNRs to evolve without reaching the ST stage. A critical ambient gas density is obtained. For densities higher than this critical value, the evolution differs significantly from the standard theory. In such cases, the remnants become radiative when the thermalization of the ejecta mass has not been concluded. Thus, the ambient density is an essential parameter on the evolution of SNRs.