The high-redshift galaxies became a distinct research field during the final decade of the20thcentury. AtthattimetheLyman-breaktechniquemadeitpossibletoidentify significant samples of such objects, and the new generation of 8 to 10-m telescopes resulted in first good spectroscopic data. Today the high-redshift galaxies have developed into one of the important topics of astrophysics, accounting for about 5–10% of the publications in the major scientific journals devoted to astronomy. Because high-redshift galaxies is a rapidly developing field and since new results are published constantly, writing a book on this topic is challenging. On the other hand, in view of the large amount of individual results now in the literature, and in view of the still growing interest in this topic, it appears worthwhile to summarize and evaluate the available data and to provide an introduction for those who wish to enter this field, or who, for various reasons, might be interested in its results. The end of the first decade of the 21st century appears to be a good point in time to attempt such a summary. The current generation of ground-based 8 to 10-m - optical telescopes, the Hubble Space Telescope, and the most important large radio telescopes have by now been in operation since about one or two decades. Although these instruments will continue to produce important scientific results for some time to come, many of the initial programs exploiting their unique new possibilities have been completed.