Let F be a positive definite binary quadratic form. One may classify such forms with fixed discriminant Δ, up to equivalence in GL2(Z) or refine this further to proper equivalence in SL2(Z). These are classical results developed by Lagrange and Gauss and lead to well-known statements about the class number h(Δ). In his paper “Über Bilineare Formen Mit Vier Variabeln”, Kronecker introduces the finer notion of complete equivalence, which is used to study the class number of positive definite forms with integer coefficients of the type ax2+2bxy+cy2. In this talk we will discuss Kronecker’s development of the class number via complete equivalence and compare it with the classical results of Lagrange and Gauss.