In this question, the original poster wrote:
On every Riemannian manifold $M$, we can consider the Hodge $*$-operator, which is characterised by the following formula: $$a\wedge *b = (a,b)\nu.$$ Here $a$ and $b$ are smooth forms on $M$, $(\ ,\ )$ is a metric on $\wedge T^*\!M$ and $\nu$ is the volume form with respect to the Riemannian metric.
I'm looking to study this formula in particular, but it's difficult to search for because of the notation.
What are a couple webpages or books that discuss (or even derive) this formula? The simpler the better.