  We study the structure of symplectic quandles, quandles which are also
R-modules equipped with an antisymmetric bilinear form. We show that every
finite dimensional symplectic quandle over a finite field F or arbitrary field
F of characteristic other than 2 is a disjoint union of a trivial quandle and a
connected quandle. We use the module structure of a symplectic quandle over a
finite ring to refine and strengthen the quandle counting invariant.
