We consider a model of weakly-interacting electrons in bilayer graphene. Bilayer graphene is a 2-dimensional crystal consisting of two layers of carbon atoms in a hexagonal lattice. Our main result is an expression of the free energy and two-point Schwinger function as convergent power series in the interaction strength. In this talk, I discuss the properties of the non-interacting model, and exhibit three energy regimes in which the energy bands are qualitatively different. I then sketch how this decomposition may be used to carry out the renormalization group analysis used to prove our main result.  Joint work with Alessandro Giuliani.