  We demonstrate the redshift-evolution of the spectral profile of H i
Lyman-alpha (Ly{\alpha}) emission from star-forming galaxies. In this first
study we pay special attention to the contribution of blueshifted emission. At
redshift z = 2.9-6.6, we compile spectra of a sample of 229 Ly{\alpha}-selected
galaxies identified with the Multi-Unit Spectroscopic Explorer at the Very
Large Telescope, while at low-z (< 0.44) we use a sample of 74
ultraviolet-selected galaxies observed with the Cosmic Origin Spectrograph
onboard the Hubble Space Telescope. At low-z, where absorption from the
intergalactic medium (IGM) is negligible, we show that the ratio of Ly{\alpha}
luminosity bluewards and redwards of line center (L_B/R) increases rapidly with
increasing equivalent width (W Ly{\alpha}). This correlation does not, however,
emerge at z = 3-4, and we use bootstrap simulations to demonstrate that trends
in L B/R should be suppressed by variations in IGM absorption. Our main result
is that the observed blueshifted contribution evolves rapidly downwards with
increasing redshift: L_B/R~30 % at z~0, but drops to 15 % at z~3, and to below
3 % by z~6. Applying further simulations of the IGM absorption to the
unabsorbed COS spectrum, we demonstrate that this decrease in the blue-wing
contribution can be entirely attributed to the thickening of intervening
Ly{\alpha} absorbing systems, with no need for additional H i opacity from
local structure, companion galaxies, or cosmic infall. We discuss our results
in light of the numerical radiative transfer simulations, the evolving total
Ly{\alpha} and ionizing output of galaxies, and the utility of resolved
Ly{\alpha} spectra in the reionization epoch.
