Selberg's central limit theorem for $\log \mathrm{\mid }\zeta (\frac{1}{2}+it)\mathrm{\mid }$

We present a new and simple proof of Selberg’s central limit theorem, according to which $\log \mathrm{\mid }\zeta (\frac{1}{2}+it)\mathrm{\mid }$ is approximately normally distributed with mean $0$ and variance $\frac{1}{2}\log \log t$.