In chapter 1 we introduce some basic elements of modern
cosmology, describing the main features of the standard hot big-bang model and the concept of
inflation. Special attention is devoted to show that recent observational data are consistent with
the theoretical framework. In chapter 2 we review the theory of gravitational instability in an
expanding universe. Both the Eulerian and the Lagrangian perturbative approaches to the evolution
of density perturbations are discussed in detail. The spherical top-hat model and a series of
dynamical approximations are also presented. Chapter 3 deals with scaling solutions to the problem
of clustering growth. After a brief review, we present some original results regarding the evolution
of the autocorrelation function of the mass density field. In particular, we test the predictions
of some empirically calibrated scaling Ansatze against the analytical solutions obtained by using
the Zel'dovich approximation. Chapter 4 is devoted to the issue of hierarchical clustering. First,
we describe the Press-Schechter theory for the abundance and mass distribution of dark matter
haloes, and its excursion-set extension. A new model for the clustering of dark haloes in Lagrangian
space is then discussed. In chapter 5 we present an astrophysical application of the Press-Schechter
formalisrn. In particular, we investigate the lensing effect of background supernovae due to mass
condensations in three popular CDM cosmologies. Our results suggest that it is not inconceivable
that new and existing search teams will soon be able to detect magnified supernovae by conducting
deep pencil beam surveys. In chapter 6 we review the theory of biased galaxy formation. Both
the original motivations that led to its formulation and recent developments are discussed. In
chapter 7 we present a new stochastic approach to the clustering evolution of dark matter halos
in Eulerian space. Our results clearly point to a characterization of the halo-to-mass biasing as a
highly non-linear and non-local process. This chapter contains some of the most important results
of this thesis. We devote chapter 8 to compare the predictions of the models introduced in chapters
4, 6 and 7 with N-body simulations. In appendix A we introduce the basic concepts of the theory
of random fields, while in appendix B we briefly summarize the main results of classical kinetic
theory. The definition of the n-point correlation functions for a population of discrete objects (e.g.
galaxies) is also given.
