Power laws : a statistical trek This monograph is a comprehensive and cohesive exposition of power law statistics. Following a bottom up construction from a foundational bedrock – the power Poisson process – this monograph presents a unified study of an assortment of power law statistics including: Pareto laws Zipf laws Weibull and Fréchet laws power Lorenz curves Lévy laws power Newcomb Benford laws sub diffusion and super diffusion and 1 f and flicker noises. The bedrock power Poisson process as well as the assortment of power law statistics are investigated via diverse perspectives: structural stochastic fractal dynamical and socioeconomic. This monograph is poised to serve researchers and practitioners – from various fields of science and engineering – that are engaged in analyses of power law statistics. Introduction From lognormal to power The Poisson law Framework Threshold analysis Hazard rates Order statistics Exponent estimation Socioeconomic analysis Fractality Sums Dynamics Limit laws First digits Back to lognormal Conclusion Appendix.