State the Seifert-Van Kampen Theorem. Deduce that if $f: S^{1} \rightarrow X$ is a continuous map, where $X$ is path-connected, and $Y=X \cup_{f} B^{2}$ is the space obtained by adjoining a disc to $X$ via $f$, then $\Pi_{1}(Y)$ is isomorphic to the quotient of $\Pi_{1}(X)$ by the smallest normal subgroup containing the image of $f_{*}: \Pi_{1}\left(S^{1}\right) \rightarrow \Pi_{1}(X)$.

State the classification theorem for connected triangulable 2-manifolds. Use the result of the previous paragraph to obtain a presentation of $\Pi_{1}\left(M_{g}\right)$, where $M_{g}$ denotes the compact orientable 2 -manifold of genus $g>0$.