  A sample of $2.8 \times 10^4$ $K^{+} \to \pi^{+} \mu^{+} \mu^{-}$ candidates
with negligible background was collected by the NA62 experiment at the CERN SPS
in 2017--2018. The model-independent branching fraction is measured to be
$(9.15 \pm 0.08)\times 10^{-8}$, a factor three more precise than previous
measurements. The decay form factor is presented as a function of the squared
dimuon mass. A measurement of the form factor parameters and their
uncertainties is performed using a description based on Chiral Perturbation
Theory at $\mathcal{O}(p^6)$.
