This book is focused on the analysis of the anomalies: an anomaly is something which is inconsistent with, or deviating from, what is usual, normal, or expected. The majority of the methods is based on a binary classification of data instances as either anomalous or not anomalous; this method creates levels of anomaly by the use ofa bayesian approach to assess the probability of occurrence of a particular data instance given a small history of data. An application of the method to returns of financial transactions is present: in this field having different degrees of anomaly can lead to bigger or smaller size for a position during high frequency trading leading to bigger profits and smaller losses.