The derived exact sequences -- Finite modules -- Realization of finite modules -- ?i of finite modules -- Product structure on finite modules -- Classification of derived product structure -- Rational invariants -- Z-torsion-free modules -- ?-only torsion -- Statement of realization theorem -- Inductive construction of derived sequences -- Inductive recovery of derived sequences -- Homogeneous and elementary modules -- Realization of elementary modules -- Classification of elementary modules -- Completion of proof -- Classification of ?-primary modules -- Classification fails in degree 4 -- Product structure on ?-primary modules -- Classification of product structure -- Realization of product structure on homogeneous modules -- Product structure on semi-homogeneous modules -- A non-semi-homogeneous module -- Rational classification of product structure -- Non-singular lattices over a Dedekind domain -- Norm criterion for a non-singular lattice -- Dedekind criterion: p-adic reduction -- A computable Dedekind criterion -- Computation of low-degree cases -- Determination of ideal class group -- The quqdratic symetric case.