Formation of the First Black holes: Formation and evolution of the cosmic large-scale structure

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.