This chapter starts with a brief recap on transformations that preserve length in three-dimensional Euclidean space. Starting with linear transformations, the real orthogonal group O(3)Orthogonal group (3) is introduced and relations between elements of this group are described using group terminology exposing proper rotations and improper rotations. The proper rotations which are orientationOrientation preserving form the special orthogonal subgroupGroupsubgroup SO(3) Special orthogonal group (3) which is a subgroup of O(3). Molecular symmetry plays a crucial role in chemistry, influencing physical properties, chemical reactivity and spectroscopy. Examples of symmetry elements (such as rotation axes, mirror planes and inversion points) are presented to illustrate molecule classification used by chemists.