  We report second- and third-harmonic generation in monolayer MoS$_\mathrm{2}$
as a tool for imaging and accurately characterizing the material's nonlinear
optical properties under 1560 nm excitation. Using a surface nonlinear optics
treatment, we derive expressions relating experimental measurements to second-
and third-order nonlinear sheet susceptibility magnitudes, obtaining values of
$|\chi_s^{(2)}|=2.0\times10^{-20}$ m$^2$ V$^{-1}$ and for the first time for
monolayer MoS$_\mathrm{2}$, $|\chi_s^{(3)}|=1.7\times10^{-28}$ m$^3$ V$^{-2}$.
These sheet susceptibilities correspond to effective bulk nonlinear
susceptibility values of $|\chi_{b}^{(2)}|=2.9\times10^{-11}$ m V$^{-1}$ and
$|\chi_{b}^{(3)}|=2.4\times10^{-19}$ m$^2$ V$^{-2}$, accounting for the sheet
thickness. Experimental comparisons between MoS$_\mathrm{2}$ and graphene are
also performed, demonstrating $\sim$3.4 times stronger third-order sheet
nonlinearity in monolayer MoS$_\mathrm{2}$, highlighting the material's
potential for nonlinear photonics in the telecommunications C band.
