The infinite series of the form $\sum_{n=1}^\infty \frac{1}{n^s}$ is called the Riemann zeta function. It was introduced in the eighteen century and has been studied extensively ever since. It is known to play an important role in many fields including number theory. For example, it is deeply connected to the distribution of prime numbers. In this talk, I will survey some properties of the Riemann zeta function and its connection to the mystery of prime numbers. Furthermore, we will touch upon a famous million-dollar conjecture called Riemann Hypothesis. All basic terms will be defined in the talk.

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