# Abstract algebra

In mathematics, more specifically algebra, **abstract algebra** or **modern algebra** is the study of algebraic structures.[1] Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term *abstract algebra* was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning.

This article includes a list of general references, but it lacks sufficient corresponding inline citations. (June 2019) |

Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures.

Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the *variety of groups*.