Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to the study of abstractions such as groups, rings, and fields.

The basic parts of algebra are called elementary algebra; the abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.

Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term algebra is also used for various algebraic structures, such as an algebra over a field, commonly called an algebra.