Conformal field theories (CFTs) are related (in Mathematics) to algebraic geometry, infinite-dimensional Lie algebras and probability, and (in Physics) to critical phenomena and string theory. From a mathematical point of view, much of the formalisation has been from the point of view of algebra – in fact using formal power series. I will give a denition of the simplest chiral or holomorphic CFT using elementary function theory. If time permits, I will also explain operator product expansions.