Abstract
In this thesis we consider sextactic points on plane algebraic curves and a 2-Hessian curve that identifies these points. This curve was first established by Cayley, and we prove that Cayley's 2-Hessian is wrong. Moreover, we correct his mistakes and give the correct defining polynomial of the 2-Hessian curve. In addition, we present a formula for the number of sextactic points on a cuspidal curve.