Omar Khayyam, the great eleventh-century Persian scientist, philosopher, and poet is generally known as the author of a small but magnificent corpus of quatrains (rubaiyats), made famous in the West thanks to the popularity of Edward Fitzgerald's translation. This well-deserved fame has, however, overshadowed his significance as a great scientist, except perhaps in some scientific circles. Recent research and critical editions of Khayyam's mathematical works have confirmed and underlined the importance of his achievements in mathematics and his impact on the progress of algebraic geometry, as well as on ono-Euclidean geometry and the theory of proportions. This standard work contains his innovative geometrical formulations, and places him firmly among the foremost mathematicians of the Middle Ages.