  This thesis examins a generalisation of polar decompositions to indefinite
inner product spaces. The necessary general theory is studied and some general
results are given. The main part of the thesis focuses on polar decompositions
with commuting factors: First, a proof for a generalisation of the link between
polar decomposition with commuting factors and normal matrices is given. Then,
some properties of such decompositions are studied and it is shown that the
commutativity of the factors only depends on the selfadjoint part. Eventually,
polar decompositions with commuting factors are studied under similarity
transformations that do not alter the structure of the space. For this purpose,
normal forms are decomposed and analysed.
