We aim to further develop Kinetic Field Theory (KFT) and apply it in particular to cosmic structure formation.KFT is a microscopic, non-equilibrium, statistical field theory for initially correlated classical particles.In its application to the formation of cosmic structures, we start with a Gaussian random field as an initial condition.Additionally we assume the interactions between individual particles to be purely gravitational, i.e. we consider structure formation of classical dark-matter particles.Starting from a recently developed mean-field approach for estimating the particle interactions, we are proposing to develop a perturbation method around the mean interaction term.We will apply these approximations to the analytic calculation of the non-linear dark-matter power spectrum of cosmic matter. The mean-field approach to interactions in KFT relies on averaging the interaction term over particle positions. To further improve the highly promising results of the mean-field approximation, we will study other, more elaborate averaging procedures.In parallel, we will pursue another approach method to the interaction term in KFT which avoids any kind of averaging procedure altogether, but immediately integrates out the time evolution, based on inertial trajectories and motivated by the Born approximation familiar from quantum mechanics.To allow investigations of cosmic structure formation in different types of dark matter, e.g. warm or axion-like dark matter, we will proceed to study how the initial power spectrum influences the final result.We will then be able to combine different mean-field approximations with a large number of initial power spectra and to apply a perturbation series around the mean-field or Born approximations to further improve the precision of the obtained results.