Abstarct: Investigation of time-dependent relativistic and non-relativistic quantum systems have been attracted many interests in last decades because investigation of these systems, yields to fundamental structure of quantum physics as well as interpretations in fields, such as gravity, optic, Pauli traps and spintronic. Because of existence of partial differential with respect coordinate and time in investigation of time evolution of time-dependent quantum systems, it has its own difficulties that in order to obviate such obstacles as well as to obtain exact or high precision solutions, different methods have been invented and utilized such as Feynman path integrals, Second quantization and Lewis-Riesenfeld dynamical invariant. In this thesis, by introducing Lewis-Riesenfeld dynamical invariant method in detail to make use of this method we want to investigate non-relativistic (such as time-dependent harmonic oscillator, many-body system, deformed nuclei and …) and relativistic (such as Fermion and free or bounded Boson systems) systems in presence of time-dependent in teractions.