The basic idea of algebra is to study what happens when numbers are added or multiplied, understand the concept of variables and how to establish polynomials and find their roots. The research object of algebra is not only numbers, but various abstract structures.

Among them, we only care about various relationships and their nature, but we don't care about the question "what is the number itself". The common types of algebraic structures are groups, rings, fields, modules, linear spaces and so on.

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"Algebra", as a proprietary mathematical term, represents a branch of mathematics. It was officially used in China, and it was first used in 1859. That year, Li, a mathematician in Qing Dynasty, and Leali, an Englishman, translated a book written by Di Yaogan, an Englishman. The name of the translation is algebra. Of course, the contents and methods of algebra have long been produced in ancient China. For example, there are equation problems in "Nine Chapters of Arithmetic".

The origin of algebra can be traced back to the Babylonian era, when people developed a more advanced arithmetic system, which enabled them to calculate by algebraic methods. Through the use of this system, they can list equations with unknowns and solve them. Nowadays these problems are generally solved by linear equations, quadratic equations and indefinite linear equations.

In contrast, most Egyptians in this period and most Indian, Greek and China mathematicians in the 1 century BC generally used geometric methods to answer such questions, such as those described in Rand's mathematical cursive book Rope Sutra, Geometry Elements and Nine Chapters of Arithmetic.

Greece's work in geometry, taking geometry as a classic, provides a framework and generalizes the formulas for solving specific problems into a more general system for describing and solving algebraic equations.