The numerical range of an operator A on a complex vector space is the set of all scalar products <AX,X> as X varies in the unit ball. It is a compact convex set in the complex plane. Geometrical properties of the numerical range imply certain properties about the operator and vice versa. We will present some basic properties and examples of numerical ranges and then focus discussion on the barycentre of the numerical range. Most of the talk will require nothing more than linear algebra.