We will introduce the Calabi and Mabuchi functionals for a Kähler class on a compact Kähler manifold. We will use these to define extremal Kähler and constant scalar curvature Kähler (cscK) metrics respectively and see the equivalent characterizations of these metrics in terms of the scalar curvature and first Chern form. We will try to look at the generalizations of both of these metrics for the top Chern form, which are called as higher extremal Kähler and higher constant scalar curvature Kähler (hcscK) metrics respectively.