  Witt rings for nondegenerate forms $\varphi$ of degree $d$ over a field of
characteristic 0 or greater than $d$ were defined by Harrison and Pareigis. We
revisit and discuss their definition as well as some special cases, classify
the $H$-forms employed in their definition, and define Witt rings of diagonal
forms of degree $d$. We also define two new Witt rings for nondegenerate forms
$\varphi$ of degree $d$.
