Al-Jabr

The Concise Book of Calculation by Restoration and Balancing (, ;{{efn|The Arabic title is sometimes condensed to Ḥisāb al-Jabr wal-Muqābalah or Kitāb al-Jabr wal-Muqābalah} or given under other transliterations.}} or ), commonly abbreviated Al-Jabr or Algebra (Arabic: ), is an Arabic-language mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath Al-Khwarizmi. It was a landmark work in the history of mathematics, with its title being the ultimate etymology of the word "algebra" itself, later borrowed into Medieval Latin as .

Al-Jabr provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree. It was the first text to teach elementary algebra, and the first to teach algebra for its own sake. It also introduced the fundamental concept of "reduction" and "balancing" (which the term al-jabr originally referred to), the transposition of subtracted terms to the other side of an equation, i.e. the cancellation of like terms on opposite sides of the equation. The mathematics historian Victor J. Katz regards Al-Jabr as the first true algebra text that is still extant. Translated into Latin by Robert of Chester in 1145, it was used until the sixteenth century as the principal mathematical textbook of European universities.