  A sample of 3120 $K^\pm\to\pi^\pm\mu^+\mu^-$ decay candidates with
$(3.3\pm0.7)%$ background contamination has been collected by the NA48/2
experiment at the CERN SPS, allowing a detailed study of the decay properties.
The branching ratio was measured to be ${\rm BR}=(9.62\pm0.25)\times 10^{-8}$.
The form factor $W(z)$, where $z=(M_{\mu\mu}/M_K)^2$, was parameterized
according to several models. In particular, the slope of the linear form factor
$W(z)=W_0(1+\delta z)$ was measured to be $\delta=3.11\pm0.57$. Upper limits of
$2.9\times 10^{-2}$ and $2.3\times 10^{-2}$ on possible charge asymmetry and
forward-backward asymmetry were established at 90% CL. An upper limit ${\rm
BR}(K^\pm\to\pi^\mp\mu^\pm\mu^\pm)<1.1\times 10^{-9}$ was established at 90% CL
for the rate of the lepton number violating decay.
