(Copyright © 2000-2001 --
this item revised 19 Nov 2000)
From Joe Chacko's 1996 FAQ:
To most people, algebra is the use of letters to represent unknown quantities in mathematical problems. 'Algebra' comes from an Arabic phrase. This referred to a particular type of mathematics that was mainly a leisure pursuit for rich men. Algebra has come a long way since then, and the algebra studied today is very far removed from the original kind.
For interested mathematicians, or advanced students, algebra becomes a more abstract subject. It involves the study of formal number systems of which the systems we use in everyday life are just examples. The set of two-by-two matrices is an example of a less common number system.