在数学中，典型群（classical group）指与欧几里得空间的对称密切相关的四族无穷多李群。术语“经典”的使用取决于语境，有一定的灵活性。这个用法可能源于赫尔曼·外尔，他的专着 Weyl (1939) 以“典型群”为题。在菲利克斯·克莱因爱尔兰根纲领的观点下，也许反映了它们和“经典”几何（classical geometry）的关系。

有时在紧群的限制下讨论典型群，这样容易处理它们的表示论和代数拓扑。但是这把一般线性群排除在外，当前都认为一般线性群是最典型的群 。

和典型李群相对的是例外李群，具有一样的抽象性质，但不属于同一类。

In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type. The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups.