This Master's thesis provides sufficient conditions under which a Non-Autonomous Dynamical System has an absolutely continuous invariant measure. The main results of this work are an extension of the Krylov-Bogoliubov theorem and Straube's theorem, both of which provide existence conditions for invariant measures of single transformation dynamical systems, to a uniformly convergent sequence of transformations of a compact metric space, which we define to be a non-autonomous dynamical system.