Assessment of financial risk requires accurate estimates of the probability of rare events. For example, in the next day of trading what is the risk of a share portfolio losing half of its value, or equivalently what is the value of the portfolio at risk of being lost with a specified probability...? Estimating the probability of such "extreme" events is challenging, as by nature they are sufficiently rare that there is little direct empirical evidence on which to base inference. Instead we have to extrapolate based on the past frequency of the occurrence of less extreme events. This module covers ideas from Extreme Value Theory which give a sound mathematical basis to such extrapolation, and shows practically how it can be used to give accurate assessments of financial risk in a range of scenarios.