  We present a generalized spin-wave theory (GSWT) for treating spin
Hamiltonians of arbitrary spin $S$. The generalization consists of an extension
of the traditional spin-wave theory from SU(2) to SU($N$). Low energy
excitations are waves of the local order parameter that fluctuates in the
SU($N$) space of unitary transformations of the local spin states, instead of
the SU(2) space of local spin rotations. Since the generators of the SU($N$)
group can be represented as bilinear forms in $N$-flavored bosons, the
low-energy modes of the GSWT are described with $N-1$ different bosons. The
generalization allows treating quantum spin systems whose ground state exhibit
multipolar ordering as well as detecting instabilities of magnetically ordered
states (dipolar ordering) towards higher multipolar orderings. We illustrate
these advantages by applying the GSWT to a bilinear-biquadratic model of
arbitrary spin $S$ on hypercubic lattices.
