  The Lyman alpha emission line is an essential diagnostic tool for probing
galaxy formation and evolution. Not only is it commonly the strongest
observable line from high-redshift galaxies but from its shape detailed
information about its host galaxy can be revealed. However, due to the
scattering nature of Lya photons increasing their path length in a non-trivial
way, if dust is present in the galaxy the line may be severely suppressed and
its shape altered. In order to interpret observations correctly, it is thus of
crucial significance to know how much of the emitted light actually escapes the
galaxy.
  In the present work, using a combination of high-resolution cosmological
hydro-simulations and an adaptively refinable Monte Carlo Lya radiative
transfer code including an advanced model of dust, the escape fractions f_esc
of Lya radiation from high-redshift (z = 3.6) galaxies are calculated. In
addition to the average escape fraction, the variation of f_esc in different
directions and from different parts of the galaxies is investigated, as well as
the effect on the emergent spectrum.
  Escape fractions from a sample of simulated galaxies of representative
physical properties are found to decrease for increasing galaxy virial mass
M_vir, from f_esc approaching unity for M_vir ~ 10^9 M_sun to f_esc less than
10% for M_vir ~ 10^12 M_sun. In spite of the dust being almost grey, it is
found that the emergent spectrum is affected non-uniformly, with the escape
fraction of photons close to the line center being much higher than of those in
the wings, thus effectively narrowing the Lya line.
