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The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters [Shectman et al. 1996]. The early Universe, however, was almost smooth, with only slight ripples seen in the cosmic microwave background radiation [Smoot et al. 1992]. Models of the evolution of structure link these observations through the effect of gravity, because the small initially overdense fluctuations attract additional mass as the Universe expands [Peebles 1980]. During the early stages, the ripples evolve independently, like linear waves on the surface of deep water. As the structures grow in mass, they interact with other in non-linear ways, more like nonlinear waves breaking in shallow water.

The expansion of the Universe renders the cosmological version of gravitational instability very slow, a power-law in time rather the exponential growth that develops in a static background. This slow rate has the important consequence that the evolved distribution of mass still retains significant memory of the initial state. This, in turn, has two consequences for theories of structure formation. One is that a detailed model must entail a complete prescription for the form of the initial conditions, and the other is that observations made at the present epoch allow us to probe the primordial fluctuations and thus test the theory.

Cosmology is now poised on the threshold of a data explosion which, if harnessed correctly, should yield a definitive answer to the question of initial fluctuations. The next generation of galaxy survey projects will furnish data sets capable answering many of the outstanding issues in this field including that of the form of the initial fluctuations. Planned CMB missions, including the Planck Surveyor, will yield higher-resolution maps of the temperature anisotropy pattern that will subject cosmological models to still more detailed scrutiny.

In these lectures I discuss the formation of large-scale structure from a general point of view, but emphasizing two of the most important gaps in our current knowledge and suggesting how these might be answered if the new data can be exploited efficiently. I begin with a general review of the theory in Section 2, discuss (briefly) possible observational developments in Section 3. Section 4 addresses the form and statistics of primordial density perturbations, particularly the question whether they are gaussian. In Section 5 I discuss uncertainties in the relationship between the distribution of galaxies and that of mass and some recent developments in the understanding of that relationship in a statistical sense.

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