"Neutrinos are the most elusive of all elementary particles and play a crucial role in astrophysics and cosmology. The three different kinds (flavors) of neutrinos can convert into each other, a macroscopic quantum effect, by their flavor mixing. These ""flavor oscillations"" are strongly modified by the feeble refractive impact of matter, a conspiracy between the very small neutrino masses and their very weak interactions. In dense astrophysical environments, notably core-collapse supernovas and the early universe, neutrinos themselves exert a refractive effect on each other, causing nonlinear feedback effects. These ""collective"" or ""nonlinear"" flavor conversions have been the subject of intense theoretical study over the past few years because they can strongly affect the neutrino signal from the next galactic supernova and flavor oscillations in the early universe. They are also of purely theoretical interest, being described by the equivalent of the pairing Hamiltonian that describes superconductivity and correlation effects in nuclei.This project ventures to develop the theory of collective flavor oscillations and applications in supernovas and the early universe to a new level of understanding. The puzzling complications caused by the lack of isotropy of the neutrinos streaming from supernovas (""multi-angle effects"") will be scrutinized with analytic and numerical techniques. The existence and importance of new instabilities will be investigated. The impact of nonstandard interactions will be included and the signatures in large-scale neutrino observatories will be studied. Furthermore, the project aims at applying these insights to the early universe where, in particular, the oscillation into yet unobserved ""sterile neutrinos"" can change the cosmic radiation and hot dark matter content."