The Schouten-Nijenhuis bracket, codifferential of products and generalized interior products of $p$-forms

Identities pertaining to the de Rham codifferential $\delta$ in differential geometry are scattered in the literature. This article gathers such formulas involving usual differential operators (Lie derivative, Schouten-Nijenhuis bracket, etc.), while adding some new ones using a natural extension of the interior product, to provide a compact handy summary