  I endeavour to provide a thorough overview of our current knowledge of
high-redshift galaxies and their evolution during the first billion years of
cosmic time, corresponding to redshifts z > 5. After first summarizing progress
with the seven different techniques which have been used to date in the
discovery of objects at z > 5, I focus thereafter on the two selection methods
which have yielded substantial samples of galaxies at early times, namely
Lyman-break and Lyman-alpha selection. I discuss a decade of progress in galaxy
sample selection at z ~ 5 - 8, including issues of completeness and
contamination, and address some of the confusion which has been created by
erroneous reports of extreme-redshift objects. Next I provide an overview of
our current knowledge of the evolving ultraviolet continuum and Lyman-alpha
galaxy luminosity functions at z ~ 5 - 8, and discuss what can be learned from
exploring the relationship between the Lyman-break and Lyman-alpha selected
populations. I then summarize what is known about the physical properties of
these galaxies in the young universe, before considering the wider implications
of this work for the cosmic history of star formation, and for the reionization
of the universe. I conclude with a brief summary of the exciting prospects for
further progress in this field in the next 5-10 years. Throughout, key concepts
such as selection techniques and luminosity functions are explained assuming
essentially no prior knowledge. The intention is that this chapter can be used
as an introduction to the observational study of high-redshift galaxies, as
well as providing a review of the latest results in this fast-moving research
field up to the end of 2011.
