The aim is to follow Manjul Barghava's papers published in Annals of Math.
"Higher Composition Laws I: A New View on Gauss Composition, and Quadratic Generalizations". vol. 159: 217–250, (2004).
"Higher Composition Laws II: On Cubic Analogues of Gauss Composition". vol. 159 (2): 865–886, (2004).
"Higher Composition Laws III: The Parametrization of Quartic Rings". vol. 159 (3): 1329–1360, (2004).
"Higher composition laws IV: The parametrization of quintic rings". vol. 167: 53–94, (2008).