  In this thesis, we study the Berkovich skeleton of an algebraic curve over a
discretely valued field $K$. We do this using coverings
$C\rightarrow{\mathbb{P}^{1}}$ of the projective line. To study these
coverings, we take the Galois closure of the corresponding injection of
function fields $K(\mathbb{P}^{1})\rightarrow{K(C)}$, giving a Galois morphism
$\overline{C}\rightarrow{\mathbb{P}^{1}}$. A theorem by Liu and Lorenzini tells
us how to associate to this morphism a Galois morphism of semistable models
$\mathcal{C}\rightarrow{\mathcal{D}}$. That is, we make the branch locus
disjoint in the special fiber of $\mathcal{D}$ and remove any vertical
ramification on the components of $\mathcal{D}_{s}$. This morphism
$\mathcal{C}\rightarrow{\mathcal{D}}$ then gives rise to a morphism of
intersection graphs $\Sigma(\mathcal{C})\rightarrow{\Sigma(\mathcal{D})}$. Our
goal is to reconstruct $\Sigma(\mathcal{C})$ from $\Sigma(\mathcal{D})$ and we
will do this by giving a set of covering and twisting data. These then give
algorithms for finding the Berkovich skeleton of a curve $C$ whenever that
curve has a morphism $\overline{C}\rightarrow{\mathbb{P}^{1}}$ with a solvable
Galois group. In particular, this gives an algorithm for finding the Berkovich
skeleton of any genus three curve. These coverings also give a new proof of a
classical result on the semistable reduction type of an elliptic curve, saying
that an elliptic curve has potential good reduction if and only if the
valuation of the $j$-invariant is positive.
