Abstract Algebra is an area of mathematics that studies algebraic structures. Some of those structures are groups, rings, fields, vector spaces, and modules.

The term abstract was added in the 20th century to distinguish it form elementary mathematics. The abstract algebra structures which often appeared during the history in other fields of mathematics, were defined rigorously using axioms and studied on their own.

The permutations are symmetrical objects that appear in the physical world. They were studied by Joseph Lagrange and Augustin Cauchy and used by Evariste Galois in finding the solutions of equations. While the permutations define implicitly groups, the notion of group was explicitly defined by Arthur Cayley in 1854.

During the 20th century, the study of abstract algebra was expanded thoroughly. New levels of abstraction, such as the theory of categories were introduced. The Bartel van der Waerden 's two volume book Modern Algebra was influential in the development of the theory.

1. Linear Algebra is a vector concept of abstract algebra
2. Contemporary and mathematical physics use abstract algebra
3. Basic ideas from number theory are necessary to study abstract algebra

• Kenyon College: Abstract Algebra Project

• HostSRV.com: The Morphism Game