  In this article, we determine the radius of univalence of sections of
normalized univalent harmonic mappings for which the range is convex (resp.
starlike, close-to-convex, convex in one direction). Our result on the radius
of univalence of section $s_{n,n}(f)$ is sharp especially when the
corresponding mappings have convex range. In this case, each section
$s_{n,n}(f)$ is univalent in the disk of radius $1/4$ for all $n\geq2$, which
may be compared with classical result of Szeg\"{o} on conformal mappings.
