  In this paper we introduce the concept of metric Clifford algebra
$\mathcal{C\ell}(V,g)$ for a $n$-dimensional real vector space $V$ endowed with
a metric extensor $g$ whose signature is $(p,q)$, with $p+q=n$. The metric
Clifford product on $\mathcal{C\ell}(V,g)$ appears as a well-defined
\emph{deformation}(induced by $g$) of an euclidean Clifford product on
$\mathcal{C\ell}(V)$. Associated with the metric extensor $g,$ there is a gauge
metric extensor $h$ which codifies all the geometric information just contained
in $g.$ The precise form of such $h$ is here determined. Moreover, we present
and give a proof of the so-called \emph{golden formula,} which is important in
many applications that naturally appear in ours studies of multivector
functions, and differential geometry and theoretical physics.
