The Riemann Zeta Function $\zeta(s)$ encodes the arithmetic properties of prime numbers, its conjectured non-vanishing outside the line $1/2+iy$ has far reaching consequences in mathematics. The values of $\zeta(m)$= $\sum_{k=1}^{\infty} k^{-m}$ at integers $m>1$ are of much interest. After describing some of the basic properties of the zeta function and some generalizations we will talk about Kontsevich's formulation of multiple zeta values as iterated integrals and the its implications to realizing the algebraic relations of multi zeta values. The goal of the talk is to bring to light the interesting phenomenon that a generalization of a zeta function to more variables can be more transparent and significant to a general mathematical audience (than the classical zeta function).

No familiarity with number theory or the zeta function is assumed in this talk.