David Eklund: Classification of integral bilinear forms

Consider a free Abelian group of finite rank equipped with a symmetric bilinear form with values in the integers. Assume that the determinant of the form is 1 or -1. In the case where the form is indefinite there is a complete classification. It says that an indefinite integral form as above is determined up to isomorphism by three invariants: rank, index and parity. I will go through the proof of this structure theorem. The definite case is more complicated, and I will discuss it if time permits.