理想类群是代数数论的基本对象之一，简称类群。它描述了一个数域的理想与元素的差异。理想类群是有限交换群，其元素个数称作该域的类数。

设 为戴德金整环。此时 中的非零理想对乘法构成一个交换幺半群。

今将定义其上的等价关系：设 为二非零理想，定义

理想幺半群对此关系的商构成一个交换群 ，称为 的理想类群。

另一套进路是考虑 的非零分式理想构成之交换群，再考虑它对主分式理想 之商，由此得到的对象自然同构于理想类群。

In mathematics, for a field K an ideal class group (or class group) is the quotient group J_K/P_K where J_K is the whole fractional ideals of K and P_K is the principal ideals of K. The extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by the ideal class group (or class group). If this group is finite (as it is in the case of the ring of integers of a number field), then the order of the group is called the class number. The multiplicative theory of a Dedekind domain is intimately tied to the structure of its class group. For example, the class group of a Dedekind domain is trivial if and only if the ring is a unique factorization domain.