The Automorphism Theorem, discovered first by Jung in 1942, asserts that if $k$ is a field, then every polynomial automorphism of $k^2$ is a finite product of linear automorphisms and automorphisms of the form $(x, y) \mapsto (x + p(y), y)$ for $p \in k[y]$. We present here a simple proof for the case $k = \mathbf{C}$ by using Newton-Puiseux expansions.