Abstract: This talk will be an explicit example of a well understood instance of deformation theory. Starting from the elementary definition of formal group laws, we will sketch a proof that the functor of formal group laws is corepresented by a polynomial ring (Lazard's Theorem). We will show that the functor of deformations of a formal group over a complete local ring with finite residue field is corepresented by rings of power series (Lubin-Tate Theory). If time permits, we will compute the automorphism ring of the deformation spaces. The methods will be homological, but the proofs are largely elementary in nature.