  For each odd $m \geq 3$ we completely solve the problem of when an $m$-cycle
system of order $u$ can be embedded in an $m$-cycle system of order $v$,
barring a finite number of possible exceptions. In cases where $u$ is large
compared to $m$, where $m$ is a prime power, or where $m \leq 15$, the problem
is completely resolved. In other cases, the only possible exceptions occur when
$v-u$ is small compared to $m$. This result is proved as a consequence of a
more general result which gives necessary and sufficient conditions for the
existence of an $m$-cycle decomposition of a complete graph of order $v$ with a
hole of size $u$ in the case where $u \geq m-2$ and $v-u \geq m+1$ both hold.
