代数是一个较为基础的数学分支。它的研究对象有许多。诸如数、数量、代数式、关系、方程理论、代数结构等等都是代数学的研究对象。

初等代数一般在中学时讲授，介绍代数的基本思想：研究当我们对数字作加法或乘法时会发生什幺，以及了解变量的概念和如何创建多项式并找出它们的根。

代数的研究对象不仅是数字，还有各种抽象化的结构。例如整数集作为一个带有加法、乘法和序关系的集合就是一个代数结构。在其中我们只关心各种关系及其性质，而对于「数本身是甚么」这样的问题并不关心。常见的代数结构类型有群、环、域、模、线性空间等。

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, 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. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).