This thesis is organised in three parts: Part 1 is concerned with a short introduction to spatially homogenous cosmology and the use of methods from the mathematical theory of dynamical systems in this research field. It aims to help the reader who is just starting to become acquainted with spatially homogenous cosmology to get a good overview and to become familiar with the basic ideas and concepts. After the lecture of part 1 the reader should then be able to read and understand part 2 at

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... t along general lines. Part 2 is a reprint of my research article Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter which was published by Springer in 2012 in the journal General Relativity and Gravitation. It deals with the analysis of one particular class of spatially homogenous cosmologies. The therefor chosen matter contents are in general anisotropic and comprise a larger family of models in which for instance also perfect fluids are contained as special cases. The results allow to draw conclusions on how the grade of anisotropy of the matter content effects the past and future asymptotic evolution of these models. Part 3 gives a tutorial on how to visualise the solutions of the evolution equations examined in part 2 in an interactive flow diagram with the computer algebra system Maple. The such produced diagrams allow the user to see a change in the behaviour of the solutions as a direct reaction to the change in the matter parameters, where one of them essentially gives the grade of matter anisotropy. They are therefore well suited to clearly represent the complex space of solutions, and most notably to present the physical conclusions which were drawn out of the analysis in a comprehensible fashion. Part 3 is also supplemented by a Maple document, which has the same content than presented in this part, with working examples.