- elementary algebra, where the properties of the real number system are recorded, symbols are used as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied
- abstract algebra, where algebraic structures such as fields, groups, and rings are axiomatically defined and investigated. The specific properties of vector spaces are studied in linear algebra.
- universal algebra, where those properties common to all algebraic structures are studied.
- computer algebra, where algorithms for the symbolic manipulation of mathematical objects are collected

- Diophantus, "father of Algebra"
- Mohammed al-Khwarizmi, who probably deserves the title more.\n