  We propose a programme for systematically counting the single and multi-trace
gauge invariant operators of a gauge theory. Key to this is the plethystic
function. We expound in detail the power of this plethystic programme for
world-volume quiver gauge theories of D-branes probing Calabi-Yau
singularities, an illustrative case to which the programme is not limited,
though in which a full intimate web of relations between the geometry and the
gauge theory manifests herself. We can also use generalisations of
Hardy-Ramanujan to compute the entropy of gauge theories from the plethystic
exponential. In due course, we also touch upon fascinating connections to Young
Tableaux, Hilbert schemes and the MacMahon Conjecture.
