abstract: In this lecture a systematic approach to wave equations with metric perturbation will be discussed based on the Minkowski null-frame. More precisely, our Lorentz metric is supposed to be a perturbation by the unknown function from the Minkowski metric, and we will examine which kind of assumption on the perturbation is necessary to guarantee the global existence result for small initial disturbance. Since this course is intended as an introductory one for undergraduate students, the only pre-requisites will be (i) the calculus (ii) basic functional analysis.