Algebra is one of the main branches of mathematics. Its subject matter is that of mathematical symbols and their manipulation. The word "algebra" is of Arabic origin, being derived from *al-jabr*, which means "restoration," and was part of the title of a book by Al Khowarizmi (from whose name comes the word "algorithm").

Historically, algebra was about the relations and properties of numbers in general, with symbols (typically letters) being used to denote numbers. Around the nineteenth century, the scope of algebra began to broaden under the influence of two new ideas. The first idea was that mathematics did not need to restrict itself to the study of number and shape, but could deal effectively with many types of entities, including vectors and matrices. The second idea was formalism, the idea that mathematics can be regarded simply as the rule-based manipulation of symbols with no inherent meaning. What resulted from these ideas was the study of algebraic structures such as groups, rings, and fields.