The world's population increases so rapidly that will place an enormous strain on energy resources. Nuclear power today represents one of the most important contributors to the word electricity supply. Disposal of nuclear waste is critical to the continuous development and future use of nuclear energy. The coupling of an external neutron source to a sub-critical reactor to compose an accelerator driven system (ADS) is a very interesting option to transmutation nuclear waste and improve the safety of nuclear critical reactor in terms of criticality control. The book provides comprehensive information about The nuclear power, nuclear waste and its transmutation strategies, theoretical foundations of the efficiency of accelerator-driven sub-critical reactors, nuclear data libraries, Monte Carlo code MCNPX and WIMS code, design and description of the basic configurations of the MYRRHA FASTEF subcritical BoL core and the MYRRHA FASTEF subcritical equilibrium core. In addition to calculating the neutronic parameters of the proposed model. The book can be used as a textbook for students of nuclear physics and engineering.