This will be a two part lecture series. In the first lecture, we give an introduction to arithmetic Kleinian groups. In the second lecture, we show that if M is an arithmetic hyperbolic 3-manifold, then the set of all rational multiples of lengths of closed geodesics of M both determines and is determined by the commensurability class of M. This implies that the spectrum of the Laplace operator of M determines the commensurability class of M.