The polarisation ellipse and the Jones vector formalism are the geometrical (three real-valued angles) and algebraic (amplitude & phase) formalisms to describe polarisation states of an electromagnetic wave. The ellipse has an orientation, an ellipticity and absolute phase angle. The three angles are integrated in one mathematical ellipse formulation that can represent linear, elliptic and circular polarisation states. The Jones vector formalism is an algebraic formulation allowing all calculus available in linear algebra. Both representations (polarisation ellipse & Jones vector) can be converted into each other seemlessly with a simple elliptical basis (special unitary SU(2)) transformation.