  This is a review of models of inflation and of their predictions for the
primordial non-Gaussianity in the density perturbations which are thought to be
at the origin of structures in the Universe. Non-Gaussianity emerges as a key
observable to discriminate among competing scenarios for the generation of
cosmological perturbations and is one of the primary targets of present and
future Cosmic Microwave Background satellite missions. We give a detailed
presentation of the state-of-the-art of the subject of non-Gaussianity, both
from the theoretical and the observational point of view, and provide all the
tools necessary to compute at second order in perturbation theory the level of
non-Gaussianity in any model of cosmological perturbations. We discuss the new
wave of models of inflation, which are firmly rooted in modern particle physics
theory and predict a significant amount of non-Gaussianity. The review is
addressed to both astrophysicists and particle physicists and contains useful
tables which summarize the theoretical and observational results regarding
non-Gaussianity.
