  Several arguments suggest parity violation may be observable in high energy
strong interactions. We introduce new analysis tools for describing the
azimuthal dependence of multi-particle distributions, or "azimuthal flow."
Analysis uses the representations of the orthogonal group O(2) and dihedral
groups $D_{N}$ necessary to define parity correctly in two dimensions.
Classification finds that collective angles used in event-by-event statistics
represent inequivalent tensor observables that cannot generally be represented
by a single "reaction plane". Many new parity-violating observables exist that
have never been measured, while many new parity-conserving observables formerly
lumped together are now distinguished. We use the concept of "event shape
sorting" to suggest separating right- and left-handed events, and we discuss
the effects of transverse and longitudinal spin. The analysis tools are
statistically robust, and can be applied equally to low or high multiplicity
events at the Tevatron, $RHIC$ or $RHIC\, Spin$, and the $LHC$.
