The Middle East was the birthplace of civilization in the region that is today called Iraq. For that reason, many contributions such as irrigation, social class, writing, and organized religion were born in the Middle East. For the purpose of this question, however, the focus will be given to the golden age of Islamic culture between the Eighth and Fourteenth Century. There was a remarkable amount of scientific achievement during this period that would ultimately make its way to the Western world through the Crusades and commerce.
During the golden age, amazing developments happened in the world of medicine. Islamic scholars introduced the concept of emergency rooms for extreme cases of trauma. Islamic hospitals were among the most advanced in the world at the time. Doctors in the Middle East were the first to recognize contagions, particularly with respect to tuberculosis and later the Bubonic Plague. Muslim scholars understood the various parts of the eye and their functions and performed cataract surgery. Many of the developments in the world of medicine would impact the future of the science moving forward.
Islamic astronomers also contributed to the understanding of the universe. During this period it was discovered that the Earth revolved around its own axis. In order to schedule prayer times, astronomers needed a way to predict sunsets and sunrises. They developed the astrolabe for this purpose. The astrolabe was also important for navigating the seas and was used by Europeans to chart new paths on the high seas. Muslim astronomers also charted the stars and constellations which was also used for navigation in the future.
In the area of mathematics, al-Khwarizmi was a pioneer and the inventor of algebra, an area of math that is named after his book. Using mathematics and astronomy, a very accurate calendar was developed that was only off by one day over five millennia.