This talk will consist roughly of three parts. In the first part I will define the the face algebra of a hyperplane arrangement and mention some motivation for its study. In the second part I will define a new (co)homology construction on posets and specialize the construction to geometric lattices of hyperplane arrangements. In the third part I will present the definition of the quiver of a basic algebra (the face algebra is a basic algebra) and describe the quiver of the face algebra. Finally, we will see how the three parts of the talk are connected. It should be fun.