  We study the geometry of horospheres in Teichm\"uller space of Riemann
surfaces of genus g with n punctures, where $3g-3+n\geq 2$. We show that every
$C^1$-diffeomorphism of Teichm\"uller space to itself that preserves
horospheres is an element of the extended mapping class group. Using the
relation between horospheres and metric balls, we obtain a new proof of
Royden's Theorem that the isometry group of the Teichm\"uller metric is the
extended mapping class group.
