  The article is part of a review volume on the formation of the first black
holes and summarises FLRW-cosmologies, the statistical description of cosmic
structures as Gaussian random fields, as well as fluid mechanics in the linear
and nonlinear regime. In particular, I review the evolution of the cosmic
large-scale structure in linear structure formation and describe how
perturbative solutions are constructed, leading to the built-up of
non-Gaussianitites. Lastly, I discuss halo formation by spherical collapse and
number densities of haloes that form in a Gaussian random field.
