The well-known analytic theory of partially polarized electromagnetic waves is complemented with a geometric theory. In the geometric theory the components of the 2 X 2 coherence matrix of a partially polarized plane wave and the Stokes parameters of the wave are treated in two four-dimensional spaces. From the first four-dimensional space a three-dimensional space is derived which constitutes a Poincare model of threedimensional (non-Euclidean) hyperbolic space having a plane, the polarization ratio plane, as the fundamental surface. This model can also be obtained by a generalization to three dimensions of an elementary inversion method called the Isometric Circle Method in the polarization ratio plane. A cross section through the second four-dimensional space, which is a Minkowski model of Lorentz space, yields the Cayley-Klein model of three-dimensional hyperbolic space having the unit sphere, in optics called the Poincare sphere, as fundamental surface. Invariant properties of partially polarized waves are studied by means of the different models. So, for example, transformations of the complex degree of correlation mu and the degree of polarization P (defined as the ratio of the polarized intensity and the total intensity) are studied in the Poincare and CayleyKlein models by means of simple geometric constructions which lucidly show the relationships between the degree of correlation and the degree of polarization. (Author).