Kushyar ibn Labban was an Iranian astronomer and mathematician who was active around 1000 A.D. His major astronomical work was a Zij [astronomical handbook with tables], called the Jami` Zij [the Comprehensive Zij]. It is written in Arabic, the scientific language in the Islamic territories in Kushyar's time, and consists of four Books: I) Elementary operations; II) Tables; III) Cosmology; IV) Proofs. My Ph.D. dissertation contains a critical edition of the original Arabic text of Books I and IV, with English translation and commentary. This work will be the first part of the complete edition, translation and commentary of Kushyar's Jami` Zij, which I hope to publish in the near future. When finished, this will be the first complete edition of the Jami` Zij and the first English translation of any complete Zij. Approximately 150 Zijes by different authors in the Islamic astronomical tradition (from the ninth to fifteenth centuries A.D.) have been preserved. A Zij usually contains tables with instructions for use for the computation of solar, lunar and planetary positions. These computations are often based on the methods of Ptolemy's Almagest (ca. 150 A.D.). Zijes are often also provided with auxiliary trigonometrical tables, tables for lunar crescent visibility and prayer times, tables of geographical and stellar coordinates, astrological tables, materials on calendars and tables for calendar conversions. The total number of tables in a single Zij may be 150-200. Up till now, little work has been done on Zijes by modern historians of science. Kushyar's Jami` Zij is interesting because it is a relatively early work, which contains separate Books III and IV on theoretical foundations (not provided in most other Zijes) and because Kushyar's own innovations made his methods somewhat different from Ptolemy's Almagest. Kushyar's chapter on calendars is of special historical interest. My edition of the Jami` Zij is based on nine different manuscripts, preserved in Istanbul (3 mss.), Cairo, Leiden (2 mss.), Berlin, Moscow and Alexandria. Only three of these manuscripts contain the entire text of the Jami` Zij.