Euler's Zeta and Double Zeta Values and Other Rational Zeta Series Representations

 In this talk, we bring into light some famous zeta values formulas due to Euler. One of them is the celebrated Basel problem $\zeta(2)=\frac{\pi^2}{6}$ which is solved completely by Euler himself in 1734. We also prove similar formulas for double zeta values and we give some rational zeta representations for $\pi$ and Apery's constant $\zeta(3)$.