  This paper is a contribution to piecewise linear (PL) symplectic topology. We
define the notion of PL symplectic manifold as being a combinatorial manifold
endowed with a piecewise constant Whitney symplectic form and investigate
possible relations between the two categories of symplectic spaces. We prove
that smooth symplectic manifolds admit arbitrarily fine smooth triangulations
in general position with respect to the symplectic form and can be
$C^0$-approximated by PL symplectic manifolds. We cannot prove that smooth
symplectic structures can be triangulated, except in trivial cases, but we can
prove that their associated volume form can be triangulated by the volume form
of some of these approximating PL manifolds.
