  The non-Gaussianity of inflationary perturbations, as encoded in the
bispectrum (or 3-point correlator), has become an important additional way of
distinguishing between inflation models, going beyond the linear Gaussian
perturbation quantities of the power spectrum. This habilitation thesis
provides a review of my work on both the theoretical and the observational
aspects of these non-Gaussianities. In the first part a formalism is described,
called the long-wavelength formalism, that provides a way to compute the
non-Gaussianities in multiple-field inflation. Applications of this formalism
to various classes of models, as well as its extensions, are also treated. In
the second part an estimator is described, called the binned bispectrum
estimator, that allows the extraction of information about non-Gaussianities
from data of the cosmic microwave background radiation (CMB). It was in
particular one of the three estimators applied to the data of the Planck
satellite to provide the currently best constraints on primordial
non-Gaussianity. Various extensions of the estimator and results obtained are
also discussed.
