(Topics in Complex Analysis IV) Classification of Singularities

We fixed some notations for the below note about classification of singularities. $D[z_0, R]$ is the open disk centered at $z_0$, and radius $R$. Furthermore, $D$ (with dot inside) $[z_0, R]$ is the punctured disk centered at $z_0$ (that is $D[z_0,R]-\{z_0\}$).