Following the discovery of the Cosmic Microwave Background (CMB) radiation, the Hot Big-Bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure (LSS) seen today. The standard Big-Bang model is an extremely successful theory, but still some crucial issues remain unsolved, such as: Where did the galaxies we see (and live in) come from and how did they evolve? We only see the 'light', but, does this trace the mass? What is the Universe made of? Cosmology is entering the precision era. In the first half of the nineties the largest three-dimensional galaxy surveys had a few thousand galaxies, in the next few years the on-going surveys such as the Sloan digital sky survey (SDSS) or the Anglo-Australian 2 degree-held survey (2dF) will have about a million galaxies. The Microwave Anisotropy Probe (MAP) and the Planck satellite will provide a map of the CMB with a resolution about two orders of magnitude better than the currently available all-sky maps. These developments will allow measurements of large scale structure and of fundamental cosmological parameters with unprecedented accuracy and therefore will allow the fundamental problems in cosmology to be addressed. To achieve these goals requires the development of new statistical techniques capable of exploiting the potential of this vast data set. These techniques are bound to be more complicated mathematically than those used up to date, but the development on the theoretical side is necessary and complementary to the huge observational effort undertaken. The main aim of my PhD has been to develop new statistical tools to extract fundamental cosmological information from these future data-sets. In particular I have been mainly concerned with two issues: how to measure the bias that is the relationship between clustering of the mass and that of galaxies and how to determine the statistical properties of the initial conditions. Theoretical models for the origin and evolution of cosmological structures, predict the clustering properties of the mass. However we can only observe luminous material (galaxies) and galaxies might be biased tracers of the underlying mass distribution. It would be possible to extract cosmological parameters such as the density parameter from large scale structure studies if galaxies were faithfully tracing the mass or if the bias was known. I present a method based on higher order statistics that would allow us to measure the bias from ongoing galaxy surveys such as the 2dF. One of the assumptions on which this method is based is that the primordial fluctuations that seeded structure formation follow a Gaussian distribution. In standard model for structure formation the primordial fluctuations are indeed Gaussian; but there are rival theories that predict very different statistics. Convincing evidence for or against Gaussian initial conditions would rule out many scenarios. I show that for physically motivated non- Gaussian models, future CMB maps in principle provide a better probe than LSS observations. However CMB and LSS probe different scales (and completely different times). I present two complementary ways to perform this test on smaller scales than CMB's, one based on higher-order statistics of future LSS data and the other based on present and future observations of high-redshift objects such as galaxies and clusters. In the next few years, from LSS and high-redshift observations and CMB maps we will be able to unveil the nature of the initial conditions, measure the bias, and consequently estimate unambiguously the density parameter of the Universe.