Arc spaces of Toric Varieties.

We are going to introduce the notion of an Arc space and discuss its basic properties. After that we will discuss several results concerning Arcs of toric varieties: some of their purely geometric properties as well as a classification of orbits of a certain natural action of a proalgebraic group on them (originating from the action of torus on a toric variety). In the latter part we will follow the works of Shihoko Ishii.