After reviewing some elementary properties of RNA, we show how the RNA folding problem can be formulated exactly in terms of an NxN matrix field theory. This formulation introduces a classification of RNA structures according to their topological genus. The large N limit of this theory generates the secondary structures of RNA (planar graphs), whereas 1/N corrections are identified as pseudo-knots. We show how the RNA structures can be analyzed in terms of primitive pseudo knots of low genus and how this concept can be included in Monte Carlo calculations to actually predict RNA folds.