  For $m \in \mathbb{N}$, we determine the irreducible components of the $m$-th
Jet Scheme of a complex branch $C$ and give formulas for their number $N(m)$
and for their codimensions, in terms of $m$ and the generators of the semigroup
of $C$. This structure of the Jet Schemes determines and is determined by the
topological type of $C$.
