In these two lectures I will give an introduction to Extreme Value Theory and its applications to dynamical systems. In the first lecture I will motivate the concept of an extreme value distribution (EVD) through an example relating to maximal cuspidal excursions of the geodesic flow on H^2/PSL(2,Z). Through this example I will give some intuition to the statement of an EVD and what consequences can be deduced from an EVD. I will then switch to an abstract statistical setting and give a basic introduction to classical Extreme Value Theory for both independent and dependent processes. In the second lecture I will cover general applications of the statistical theory to dynamical systems as well as the most recent developments in the field.