不变量理论是数学的一个分支，它研究群在代数簇上的作用。不变量理论的古典课题是研究在线性群作用下保持不变的多项式函数。

对于有限群，不变量理论与伽罗瓦理论有密切联系，一个较早的结果涉及了对称群 在多项式环 上的作用： 作用下的不变量构成一个子环，由基本对称多项式生成，由于基本对称多项式彼此代数独立，此不变量环本身也同构于另一多项式环。Chevalley-Shephard-Todd 定理刻划了其不变量环同构于多项式环的有限群。晚近的研究则更关切算法问题，例如计算不变量环的生成元，或给出其次数的上界。

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. For example, if we consider the action of the special linear group SL_n on the space of n by n matrices by left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SL_n.