  In this lecture we address three different but related aspects of the initial
continuous fluctuation field in standard cosmological models. Firstly we
discuss the properties of the so-called Harrison-Zeldovich like spectra. This
power spectrum is a fundamental feature of all current standard cosmological
models. In a simple classification of all stationary stochastic processes into
three categories, we highlight with the name ``super-homogeneous'' the
properties of the class to which models like this, with $P(0)=0$, belong. In
statistical physics language they are well described as glass-like. Secondly,
the initial continuous density field with such small amplitude correlated
Gaussian fluctuations must be discretised in order to set up the initial
particle distribution used in gravitational N-body simulations. We discuss the
main issues related to the effects of discretisation, particularly concerning
the effect of particle induced fluctuations on the statistical properties of
the initial conditions and on the dynamical evolution of gravitational
clustering.
