A central goal of observational cosmology is to characterize the statistics of the initial perturbations of our universe, thereby constraining the physics which generated them. Observations to date are consistent with adiabatic, Gaussian, scalar initial conditions but deviation from a scale invariant initial power spectrum has been observed with 3 sigma significance. This led to a new and powerful probe of the origin and evolution of structures in the universe: primordial non-Gaussianity. The latter is an actively developed field and concerns primordial non-Gaussian contributions to the correlations of cosmological fluctuations and other cosmological observables and are widely expected to become an important probe of both the early and the late universe. In particular, on-going and future observations of fluctuations in the cosmic microwave background and the large-scale structure will test the level of primordial non- Gaussianity and therefore provide us with crucial information about the early and late evolution of our universe.We plan to pursue a number of related directions of research. In particular: (1) We will employ field theoretic methods to study non-Gaussianity sourced by particular field theory models on curved spacetime. (2) We will investigate non Gaussian perturbations generated during the inflationary de Sitter phase of the Universe by using Conformal Field Theory techniques. (3) We will perform analytical and numerical work (if needed) to evaluate the non-Gaussianity left imprinted in the cosmic microwave background anisotropies by the second-order effects where the non-Gaussianity is not only of primordial origin but receives contributions from cosmological perturbations in the post-inflationary era, and (4) We will investigate the effect of heavy massive fields of the quasi-de Sitter phase of the universe on the non-Gauusianity of the primordial perturbations due to their ultraviolet mixing with light fields.