  Kinetic Field Theory (KFT) is a statistical field theory for an ensemble of
point-like classical particles in or out of equilibrium. We review its
application to cosmological structure formation. Beginning with the
construction of the generating functional of the theory, we describe in detail
how the theory needs to be adapted to reflect the expanding spatial background
and the homogeneous and isotropic, correlated initial conditions for cosmic
structures. Based on the generating functional, we develop three main
approaches to non-linear, late-time cosmic structures, which rest either on the
Taylor expansion of an interaction operator, suitable averaging procedures for
the interaction term, or a resummation of perturbation terms. We show how an
analytic, parameter-free equation for the non-linear cosmic power spectrum can
be derived.
  We explain how the theory can be used to derive the density profile of
gravitationally bound structures and use it to derive power spectra of cosmic
velocity densities. We further clarify how KFT relates to the BBGKY hierarchy.
We then proceed to apply kinetic field theory to fluids, introduce a
reformulation of KFT in terms of macroscopic quantities which leads to a
resummation scheme, and use this to describe mixtures of gas and dark matter.
We discuss how KFT can be applied to study cosmic structure formation with
modified theories of gravity. As an example for an application to a
non-cosmological particle ensemble, we show results on the spatial correlation
function of cold Rydberg atoms derived from KFT.
