This project NeuTrAE is aimed to advance our understanding on lingering puzzles on the flavor evolution of neutrinos and their implication in particle and nuclear astrophysics. Neutrinos are characterized by their flavors that can change as they propagate in a phenomenon known as neutrino flavor oscillations. The oscillations in vacuum and ordinary matter are well understood and confirmed by several experiments. Astrophysical compact objects, such as core-collapse supernovae and the violent merger event of two neutron stars or a neutron star and a black hole, are profuse sources of neutrinos. In those astrophysical environments the neutrino flux becomes so intense that the flavor interference of neutrinos with each other has to be taken into account. This non-linear effect coupling neutrinos propagating in different directions and with different energies is known as collective neutrino oscillations. Accounting for the collective neutrino oscillations in simulations of astrophysical environments requires a quantum kinetic transport. It remains a tremendous challenge due to the high-dimensionality of the problem and the vastly different scales for flavor and hydrodynamical evolution. The impact of neutrino flavor transitions on those compact objects remains elusive without efficient and sophisticated treatments. I propose the project NeuTrAE providing a pipeline to study the impact of collective neutrino oscillations in astrophysical environments. It consists of three steps: performing neutrino quantum kinetic simulations, developing numerically effective schemes that can be incorporated in state-of-the art hydrodynamical simulations, and assessing the impact of neutrino flavor transformations on heavy element nucleosynthesis and its electromagnetic signatures. NeuTrAE will also commit to significant advance on dynamical evolution of astrophysical compact objects.