  In this article we present Pickands theorem and his double sum method. We
follow Piterbarg's proof of this theorem. Since his proof relies on general
lemmas we present a complete proof of Pickands theorem using Borell inequality
and Slepian lemma. The original Pickands proof is rather complicated and is
mixed with upcrossing probabilities for stationary Gaussian processes. We give
a lower bound for Pickands constant.
