This chapter describes how large-scale structure -- the distribution of galaxies on the sky -- can be used to probe the cosmological model. We start by defining the density perturbation and its most fundamental statistical property -- the correlation function. We briefly review the evolution of density perturbations in the standard cosmological model, emphasizing key results. We next discuss the growth of cosmic structure, and segue into talking about the power spectrum of density perturbations, its theoretical description, and its measurements. This leads us to discuss structure formation in the universe more generally, the role of numerical (N-body) simulations, and the mass function. We end by discussing how the statistical properties of dark-matter halos, which can easily be modeled in simulations, are related to those of galaxies that we typically observe.

In this chapter we present the analysis of the large scale matter distribution within linear perturbation theory in a fully relativistic way. We take into account that only directions and redshifts are observable while lengths scales are always inferred from a cosmological model. We first introduce the traditional density and redshift space distortion contribution to the observed uctuations and then proceed to discuss the smaller lensing and large scale relativistic terms. We express the clustering properties of matter in terms of directly observable quantities and study their scale and redshift dependence. We also discuss ‘intensity mapping’ a new observational technique which will hopefully bear fruit in the near future. Also this chapter has been newly added in the second edition.