This thesis focuses on a finite-temperature field-theoretical treatment of neutrino oscillations in hot and dense media. By implementing the methods of real-time non-equilibrium field theory, we study the dynamics of neutrino mixing, oscillations, decoherence and relaxation in astrophysical and cosmological environments. We first study neutrino oscillations in the early universe in the temperature regime prior to the epoch of Big Bang Nucleosynthesis (BBN). The dispersion relations and mixing angles in the medium are found to be helicity-dependent, and a resonance like the Mikheyev-Smirnov-Wolfenstein (MSW) effect is realized. The oscillation time scales are found to be longer near a resonance and shorter for off-resonance high-energy neutrinos. We then investigate the space-time propagation of neutrino wave-packets just before BBN. A phenomenon of "frozen coherence" is found to occur if the longitudinal dispersion catches up with the progressive separation between the mass eigenstates, before the coherence time limit has been reached. However, the transverse dispersion occurs at a much shorter scale than all other possible time scales in the medium, resulting in a large suppression in the transition probabilities from electron-neutrino to muon-neutrino. We also explore the possibility of charged lepton mixing as a consequence of neutrino mixing in the early Universe. We find that charged leptons, like electrons and muons, can mix and oscillate resonantly if there is a large lepton asymmetry in the neutrino sector. We study sterile neutrino production in the early Universe via active-sterile oscillations. We provide a quantum field theoretical reassessment of the quantum Zeno suppression on the active-to-sterile transition probability and its time average. We determine the complete conditions for quantum Zeno suppression. Finally, we examine the interplay between neutrino mixing, oscillations and equilibration in a thermal medium, and the corresponding non-equilibrium dynamics
