Elementary algebra, also known as college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variables.
A typical algebra problem.
Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
The Rhind Papyrus from ancient Egypt, dated around 1650 BCE, is one of the earliest documents discussing algebraic problems.
Al-Khwarizmi's The Compendious Book on Calculation by Completion and Balancing provided a general account of how linear and quadratic equations can be solved through the methods of "reducing" and "balancing".
Garrett Birkhoff developed many of the foundational concepts of universal algebra.
Image: Francois Viete