  We consider an infinitesimal volume where there are many rigid molecules of
the same kind, and discuss the description and classification of the local
anisotropy in this volume by tensors. First, we examine the symmetry of a rigid
molecule, which is described by a point group in $SO(3)$. For each point group
in $SO(3)$, we find the tensors invariant under the rotations in the group.
These tensors shall be symmetric and traceless. We write down the explicit
expressions. The order parameters to describe the local anisotropy are then
chosen as some of the invariant tensors averaged about the density function.
Next, we discuss the classification of local anisotropy by the symmetry of the
whole infinitesimal volume. This mesoscopic symmetry can be recognized by the
value of the order parameter tensors in the sense of maximum entropy state. For
some sets of order parameter tensors involving different molecular symmetries,
we give the classification of mesoscopic symmetries, in which the three-fold,
four-fold and polyhedral symmetries are examined.
