In the Middle Ages the astrolabe was the best known and most widely used astronomical instrument both in the Islamic world and in the West. The oldest extant description of the construction of this instrument was written by the well-known Arabic astronomer al-Farghani (Baghdad, ca. 856). His treatise is especially valuable because of the tables it contains to enable an artificer to draw the various circles and arcs on the instrument. The Arabic text of this work, including the tables, is presented here for the first time in a critical edition, accompanied by an English translation and a commentary reproducing al-Farghani's reasoning in modern mathematical notation.