State the Van Kampen Theorem. Use this theorem and the fact that $\pi_{1} S^{1}=\mathbb{Z}$ to compute the fundamental groups of the torus $T=S^{1} \times S^{1}$, the punctured torus $T \backslash\{p\}$, for some point $p \in T$, and the connected sum $T \# T$ of two copies of $T$.