Abstract : The most important function in all of number theory is undoubtedly the Riemann Zeta function which is a concise package of practically all information about primes. The function is at first defined for real arguments $\sigma > 1$ by the convergent infinite series $\zeta (\sigma) = \sum_{1 \leq n \leq \infty} n^{\sigma}$. The evaluation of $\zeta$ at integers was a question that attracted considerable attention in the eighteenth century. Euler came up with the first evaluation viz. $\zeta (2) = \pi^2/6$ and went on to evaluate the function at all even integers. For the values of $\zetz$ at odd integers we have only some weak qualitative results. Riemann showed in a seminal work that there is indeed a meromorphic function $\zeta$ in $\C - \{1\}$ which equals the function defined by the series above on the set $\{x \in \R \ | \ x > 1\} $. It is Riemmann's work on the $\zeta$ function that brought it to the heart of Number Theory.