L\"uscher's method is routinely used to determine meson-meson, meson-baryon
and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from
Lattice QCD calculations - presently at unphysical light-quark masses. In this
work we review the formalism and develop the requisite expressions to extract
phase-shifts describing meson-meson scattering in partial-waves with
angular-momentum l<=6 and l=9. The implications of the underlying cubic
symmetry, and strategies for extracting the phase-shifts from Lattice QCD
calculations, are presented, along with a discussion of the signal-to-noise
problem that afflicts the higher partial-waves.Comment: 79 pages, 41 figure
