No doubt that Islam once ruled the world. Its spread from the desert Madinah, where it got mature and established, to the other parts of the world compared to the short time it achieved such advancement remain a mystery hitherto. During its reign, contrary to the wide spread blasphemous teachings by its enemies, it achieved so much and made forth numerous contributions to human civilization upon which most of our today's developments are built on.
The Islamic world made important advances in science, such as in algebra, chemistry, geology etc. These where later transmitted from the Muslim world then to the West. History has it that Stefan of Pise translated into Latin around 1127 an Arab manual of medical theory. The method of algorism for performing arithmetic with Indian-Arabic numerals was developed by the great Muslim scholar, al-Khwarizmi, a Persian Muslim (hence the word “Algorithm”) in the 9th century. This was introduced to the Europe by Leonardo Fibonacci (1170–1250). There is a translation of the Algebra by al-Khwarizmi was rendered by Robert of Chester and was known as early as 1145.
In the field of optical sciences, Ibn al-Haytham (Alhazen, 980–1037) compiled treatises on it, which were used as references by known major modern scientists like Newton and Descartes. Medical sciences were also highly developed in Islam as testified by the Crusaders, who relied on Arab doctors on numerous occasions dyring their varying courses of interacting with the then Muslim world. Joinville reports he was saved in 1250 by a “Saracen” doctor. 
It is known that every scholar or individual enthusiastic about making some inputs to the developments of his time, they spend the best they have to achieve their goals. They are known for not minding what it may cost them to get one thing or the other they see might one way or the other help in their quests. This was the same to scholars like Gerard of Cremona and others who had contributing to the growth of European science through new learning as their major search. These scholars were interested in ancient Greek philosophical and scientific texts (notably the Almagest) which were not obtainable in Latin in Western Europe, but had survived and been translated into Arabic in the Muslim world. Gerard was said to have made his way to Toledo in Spain and learnt Arabic specifically because of his "love of the Almagest". While there, he took advantage of the "abundance of books in Arabic on every subject". These scholars translated many scientific and philosophical texts from Arabic into Latin. Gerard personally translated 87 books from Arabic into Latin, including the Almagest, and also Muhammad ibn Musa al-Khwarizmi's On Algebra and Almucabala, Jabir ibn Aflah's Elementa Astronomica, al-Kindi's On Optics, Ahmad ibn Muhammad ibn Kathir al-Farghani's On Elements of Astronomy on the Celestial Motions, al-Farabi's On the Classification of the Sciences, the chemical and medical works of Rhazes, the works of Thabit ibn Qurra and Hunayn ibn Ishaq, and so many others.
The world wide web Wikipedia communication has it in its Islamic Contributions to Medieval Europe that Islam made so much of contributions to the science of the Europe. Among others, it has the following:
Western alchemy was directly dependent upon Arabic sources. The Latin alchemical works of "Geber" were standard texts for European alchemists. The exact attribution of these works remains a matter of some controversy. Some are undoubtedly translations from Arabic from works attributed to Jabir ibn Hayyan, including the Kitab al-Kimya (titled Book of the Composition of Alchemy in Europe), translated by Robert of Chester (1144); and the Book of Seventy, translated by Gerard of Cremona (before 1187). Whether these were actually written by one man (or whether indeed Jābir was a real historical figure) is disputed, but there is no doubting the influence on medieval European alchemy of the translated Arabic works. (A few of the Latin works are now attributed to a Pseudo-Geber, as although attributed to "Geber", they have no identified Arabic source and appear to have been composed in Latin in the 13th century).
The alchemical works of Muhammad ibn Zakariyya Razi (Rhazes) were translated into Latin around the 12th century. Several technical arabic words from Arabic alchemical works, such as alkali, found their way into various European languages and became part of scientific vocabulary.
Astronomy and Mathematics:
The translation of Al-Khwarizmi's work greatly influenced mathematics in Europe. As Professor Victor J. Katz writes: "Most early algebra works in Europe in fact recognized that the first algebra works in that continent were translations of the work of al-Khwärizmï and other Islamic authors. There was also some awareness that much of plane and spherical trigonometry could be attributed to Islamic authors". The words algorithm, deriving from Al-Khwarizmi's Latinized name Algorismi, and algebra, deriving from the title of his AD 820 book Hisab al-jabr w'al-muqabala, Kitab al-Jabr wa-l-Muqabala ("The Compendious Book on Calculation by Completion and Balancing") are themselves Arabic loanwords. This and other Arabic astronomical and mathematical works, such as those by al-Battani and Muhammad al-Fazari's Great Sindhind (based on the Surya Siddhanta and the works of Brahmagupta). were translated into Latin during the 12th century.
Al-Khazini's Zij as-Sanjari (1115–1116) was translated into Greek by Gregory Choniades in the 13th century and was studied in the Byzantine Empire. The astronomical modifications to the Ptolemaic model made by al-Battani and Averroes led to non-Ptolemaic models produced by Mo'ayyeduddin Urdi (Urdi lemma), Nasir al-Din al-Tusi (Tusi-couple) and Ibn al-Shatir, which were later adapted into the Copernican heliocentric model. Abu al-Rayhan al-Biruni's Ta'rikh al-Hind and Kitab al-qanun al-Mas’udi were translated into Latin as Indica and Canon Mas’udicus respectively.
Fibonacci presented the first complete European account of the Hindu-Arabic numeral system from arabic sources in his Liber Abaci (1202). Al-Jayyani's The book of unknown arcs of a sphere (a treatise on spherical trigonometry) had a "strong influence on European mathematics". Regiomantus' On Triangles (c. 1463) certainly took his material on spherical trigonometry (without acknowledgement) from Arab sources. Much of the material was taken from the twelfth-century work of Jabir ibn Aflah (otherwise known as Geber), as noted in the sixteenth century by Gerolamo Cardano.
A short verse used by Fulbert of Chartres (952-970 –1028) to help remember some of the brightest stars in the sky gives us the earliest known use of Arabic loanwords in a Latin text: "Aldebaran stands out in Taurus, Menke and Rigel in Gemini, and Frons and bright Calbalazet in Leo. Scorpio, you have Galbalagrab; and you, Capricorn, Deneb. You, Batanalhaut, are alone enough for Pisces."
One of the most important medical works to be translated was Avicenna's The Canon of Medicine (1025), which was translated into Latin and then disseminated in manuscript and printed form throughout Europe. It remained a standard medical textbook in Europe until the early modern period, and during the 15th and 16th centuries alone, The Canon of Medicine was published more than thirty-five times. Avicenna noted the contagious nature of some infectious diseases (which he attributed to "traces" left in the air by a sick person), and discussed how to effectively test new medicines. He also wrote The Book of Healing, a more general encyclopedia of science and philosophy, which became another popular textbook in Europe. Muhammad ibn Zakariyya Razi (al-Razi) wrote the Comprehensive Book of Medicine, with its careful description of and distinction between measles and smallpox, which was also influential in Europe. Abu al-Qasim al-Zahrawi (also known as Albucasis) wrote Kitab al-Tasrif, an encyclopedia of medicine which was particularly famed for its section on surgery. It included descriptions and diagrams of over 200 surgical instruments, many of which he developed. The surgery section was translated into Latin by Gerard of Cremona in the 1100s, and used in European medical schools for centuries, still being reprinted in the 1770s.
One of the most important scientific works to be translated was Ibn al-Haytham (Alhazen)'s Book of Optics (1021). Alhazen's book was notable for his early use of an experiment based scientific method, in which he developed a theory of vision and light which built on the work of the Roman writer Ptolemy (but which rejected Ptolemy's theory that light was emitted by the eye, insisting instead that light rays entered the eye), and was the most significant advance in this field until Kepler. The Book of Optics was an important stepping stone in the history of the scientific method and history of optics. The Latin translation of the Book of Optics influenced the works of many later European scientists, including Roger Bacon and Johannes Kepler. The book also influenced other aspects of European culture. In religion, for example, John Wycliffe, the intellectual progenitor of the Protestant Reformation, referred to Alhazen in discussing the seven deadly sins in terms of the distortions in the seven types of mirrors analyzed in De aspectibus. In literature, Alhazen's Book of Optics is praised in Guillaume de Lorris' Roman de la Rose. In art, the Book of Optics laid the foundations for the linear perspective technique and may have influenced the use of optical aids in Renaissance art (see Hockney-Falco thesis). These same techniques were then employed in European geographical maps made by cartographers such as Paolo Toscanelli during the Age of Exploration.
The theory of motion developed by Avicenna from Aristotelian physics may have influenced Jean Buridan's theory of impetus (the ancestor of the inertia and momentum concepts) The work of Galileo Galilei on classical mechanics (superseding Aristotelian physics) was also influenced by earlier medieval physics writers, including Avempace. Fields of physics studied included optics and magnetism, mechanics (including statics, dynamics, kinematics and motion), and astronomy.
 Fielding H. Garrison, An Introduction to the History of Medicine: with Medical Chronology, Suggestions for Study and Bibliographic Data, p. 86
 C. Burnett, "Arabic-Latin Translation Program in Toledo", p. 255.