**Algebra** is Arabic word **“aljabr”** literally meaning **“reunion of broken parts”** it is one of the branch mathematics, together with number theory, geometry and analysis. In its most general form, It is the study of mathematical symbols and the rules for manipulating these symbols;^{} it is a unifying thread of almost all of mathematics. ^{}It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more 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. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an **“algebra”. **A mathematician who does research in algebra is called an **A****lgebraist**.

## Different Areas of Algebra in Mathematics

Some areas of mathematics that fall under the classification abstract algebra have the word algebra in their name; linear algebra is one example. Others do not: group theory, ring theory, and field theory are examples. In this section, we list some areas of mathematics with the word “algebra” in the name.

**Elementary algebra:**the part of algebra that is usually taught in elementary courses of mathematics.**Abstract algebra:**in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.**Linear algebra:**in which the specific properties of linear equations, vector spaces and matrices are studied.**Boolean algebra:**a branch of algebra abstracting the computation with the truth values*false*and*true*.**Commutative algebra:**the study of commutative rings.**Computer algebra:**the implementation of algebraic methods as algorithms and computer programs.**Homo logical algebra:**the study of algebraic structures that are fundamental to study topological spaces.