In this work we give a detailed discussion of the basic theory and current observational status of cosmology. We introduce gauge-invariant perturbation theory to derive the linear perturbation equations and use a matrix formalism to find suitable initial conditions for numerical integration. With the cosmological software package Cmbeasy we compute model predictions and compare these with experimental data. For constraining cosmological models quickly and conveniently we employ Markov Chain Monte Carlo simulation. We describe both the theory and the specific implementation in Cmbeasy. These tools are then used to constrain a standard LambdaCDM cosmology and a model with a non-zero equation of state of dark matter. We also consider the effect of a variation of the fundamental couplings on primordial element abundances, introducing a model-independent formulation that may be used to obtain predictions for any given model that relates the fundamental couplings to each other.
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