在晶体学中，晶体学点群是对称操作（例如旋转、反映）的集合。这些操作以固定的中心向其他方向移动能使晶体复原，因此称为对称操作。对于一种真正的晶体（不是准晶体），点群对应的操作必须能够保持晶体的三维平移对称性。经过它的点群中任何操作之后，晶体的宏观性质依然和操作前完全相同。在晶体的分类中，每一种点群也称为晶类。

这样看来似乎有无穷多种三维点群。然而，根据晶体局限定理可知，无穷多族的普通点群可以概括成32种晶体学点群。这32种点群与1830年约翰·弗里德里希·克里斯蒂安·赫塞尔提出的32种晶体形态学（外部）对称性是等价的，而他是从观察晶体外形得出的此结论。

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind. For a periodic crystal (as opposed to a quasicrystal), the group must also be consistent with maintenance of the three-dimensional translational symmetry that defines crystallinity. The macroscopic properties of a crystal would look exactly the same before and after any of the operations in its point group. In the classification of crystals, each point group is also known as a crystal class.