1. A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
2. A set together with a pair of binary operations defined on the set. Usually, the set and the operations include an identity element, and the operations are commutative or associative.

[Middle English, bone-setting, and Italian, algebra, both from Medieval Latin, from Arabic al-jabr (wa-l-muqābala), the restoration (and the compensation), addition (and subtraction) : al-, the + jabr, bone-setting, restoration (from jabara, to set (bones), force, restore).]

The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.