Al-Khwarizmi and his colleagues, the Banu Musa, were scholars at The House of Wisdom in Baghdad. Their task there included the translation of Greek scientific manuscripts. In addition, they worked on algebra, geometry, and astronomy. Under the patronage of Al-Mamum, he dedicated two of his texts to the Caliph- his treatise on algebra and on astronomy. The algebra treatise- Hiss al-jabr w'al-muqabala, was his most known and significant of all of his works. It is this text that gives us the word "algebra" and is the first known book written on algebra. Here is a translation of al-Khwarizmi's own words telling his purpose on writing the book:
what is easiest and most useful, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, other of various sorts and kinds are concerned.
The first section of the book is merely a discussion of what we perceive as algebra today. The book was highly practical and algebra was introduced to solve everyday problems in the Islam Empire at the time. Here is another quote describing his formula of new depth and abstraction:
When I consider what people generally want in calculating, I found that it is always a number. I also observed that any number composed of units and that any number may be divided into units. Moreover, I found that every number may be expressed from one to ten,...