This volume provides a unique primary source on the history and philosophy of mathematics and science from the mediaeval Arab world. The fourth volume of A History of Arabic Sciences and Mathematics is complemented by three preceding volumes which focused on infinitesimal determinations and other chapters of classical mathematics. This book includes five main works of the polymath Ibn al-Haytham (Alhazen) on astronomy, spherical geometry and trigonometry, plane trigonometry and studies of astronomical instruments on hour lines, horizontal sundials and compasses for great circles. In particular, volume four examines: the increasing tendency to mathematize the inherited astronomy from Greek sources, namely Ptolemy's Almagest; the development of celestial kinematics; new research in spherical geometry and trigonometry required by the new kinematical theory; the study on astronomical instruments and its impact on mathematical research. These new historical materials and their mathematical and historical commentaries contribute to rewriting the history of mathematical astronomy and mathematics from the 11th century on. Including extensive commentary from one of the world's foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research.