Algebra is a branch of Mathematics which studies Structure and Quantity. It may be roughly characterized as a generalization and abstraction of Arithmetic, in which operations are performed on symbols rather than numbers. It includes Elementary algebra, taught to high school students, as well as Abstract algebra which covers such structures as groups, rings and fields. Along with Geometry and analysis, it is one of the three main branches of mathematics.
Indian mathematician, Aryabhata (476 AD) obtained whole number solutions to linear equations by a method equivalent to the modern one. Bhaskara II (1114 AD), who wrote the text Bijaganita (algebra), was the first to recognize that a positive number has two square roots. The Hindus recognized that quadratic equations have two roots, and included negative as well as Irrational roots. They treated indeterminate quadratic equations.
The word algebra is derived from the name of the treatise first written by Persian mathematician Khwarazmi in 820 AD titled: Ketāb e mukhtasar dar Hesab o Jabr o Mughabeleh meaning The book of summary concerning calculating by transposition and reduction. The word al-jabr (from which algebra is derived) means "reunion", "connection" or "completion".The name given by the Persian/Iranian scientist Khwarazmi. It entered English via Spanish.
Algebra was introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci in 1202.
In advanced studies, axiomatic algebraic systems like groups, rings, fields, and algebras over a field are investigated in the presence of a natural geometric structure (a Topology) which is compatible with the algebraic structure. The list includes