We investigate neutrino flavor transformation in the early universe in the presence of a lepton asymmetry, focusing on a two-flavor system with 1 - 3 mixing parameters. We identify five distinct regimes that emerge in an approximate treatment neglecting collisions as the initial lepton asymmetry at high temperature is varied from values comparable to current constraints on the lepton number down to values at which the neutrino-neutrino forward-scattering potential is negligible. The characteristic phenomena occurring in these regimes are (1) large synchronized oscillations, (2) minimal flavor transformation, (3) asymmetric (neutrino- or antineutrino-only) MSW, (4) partial MSW, and (5) symmetric MSW. We examine our numerical results in the framework of adiabaticity, and we illustrate how they are modified by collisional damping. Finally, we point out the existence of matter-neutrino resonances in the early universe and show that they suffer from non-adiabaticity.