在代数数论中，二次域是在有理数域上次数为二的数域。二次域可以唯一地表成，其中无平方数因数。若，称之为实二次域；否则称为虚二次域或复二次域。虚实之分在于是否为全实域

二次域的 研究肇源甚早，起初是作为二次型理论的一支。二次域是代数数论的基本对象之一，虽然如此，至今仍有一些未解猜想，如类数问题。

In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q, the rational numbers. The map d ↦ Q(√d) is a bijection from the set of all square-free integers d ≠ 0, 1 to the set of all quadratic fields. If d > 0 the corresponding quadratic field is called a real quadratic field, and for d < 0 an imaginary quadratic field or complex quadratic field, corresponding to whether it is or not a subfield of the field of the real numbers.