**Title**: A-Homotopy Theory and Universal Covers

**Abstract**: A-homotopy theory is a homotopy theory developed for graphs. We would like to know if this homotopy relation gives the weak equivalences of a model structure on the category of graphs. We are trying to develop a weak factorization system on graphs as a stepping-stone to this goal. One requirement of a weak factorization system is the ability to factor a morphism into two morphisms from different classes. In order to do this, we are mimicking a strategy found in the homotopy theory of topological spaces that involves covering spaces and lifting properties. In this talk, I will give the construction of the universal cover of a graph.