In quantum mechanics the free rotation of a molecule is quantized, so that the rotational energy and the angular momentum can take only certain fixed values, which are related simply to the moment of inertia, , of the molecule. For any molecule, there are three moments of inertia: ,  and  about three mutually orthogonal axes A, B, and C with the origin at the center of mass of the system. The general convention, used in this article, is to define the axes such that , with axis  corresponding to the smallest moment of inertia. Some authors, however, define the  axis as the molecular rotation axis of highest order.
The particular pattern of energy levels (and, hence, of transitions in the rotational spectrum) for a molecule is determined by its symmetry. A convenient way to look at the molecules is to divide them into four different classes, based on the symmetry of their structure. These are