Definition: a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
Anyone who has unpleasant memories of slogging through this branch of mathematics will be relieved to know that the pain you felt in trying to figure out the quadratic equation is mirrored in the word’s etymology – it comes from the Arabic al-jabr, which means "the bonesetting." It should be noted, however, that algebra did not literally have anything to do with broken bones, or with the setting of the same. Instead, it was probably chosen because this connotation of "reuniting" described the act of completing the square in a quadratic equation.