Algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Elementry algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given in education to the study of algebraic structures such as groups, rings, and fields. Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry and has many practical applications. There are many areas of mathematics that belong to algebra, some having "algebra" in their names, such as commutative algebra and some not, such as Galois theory.
