His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations. He is considered the founder of algebra, a credit he shares with Diophantus. In the twelfth century, Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world. He revised Ptolemy's Geography and wrote on astronomy and astrology.

His contributions had a great impact on language. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name. His name is the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.