  We introduce numerical methods for the approximation of the main (global)
quantities in Pluripotential Theory as the \emph{extremal plurisubharmonic
function} $V_E^*$ of a compact $\mathcal L$-regular set $E\subset \C^n$, its
\emph{transfinite diameter} $\delta(E),$ and the \emph{pluripotential
equilibrium measure} $\mu_E:=\ddcn{V_E^*}.$
  The methods rely on the computation of a \emph{polynomial mesh} for $E$ and
numerical orthonormalization of a suitable basis of polynomials. We prove the
convergence of the approximation of $\delta(E)$ and the uniform convergence of
our approximation to $V_E^*$ on all $\C^n;$ the convergence of the proposed
approximation to $\mu_E$ follows. Our algorithms are based on the properties of
polynomial meshes and Bernstein Markov measures.
  Numerical tests are presented for some simple cases with $E\subset \R^2$ to
illustrate the performances of the proposed methods.
