Anomaly detection corresponds to discovery of events that typically do not conform to expected normal behavior. Such events are often referred to as anomalies, outliers, exceptions, deviations, aberrations, surprise, peculiarities or contaminants in different application domains Detection of anomalies is a common problem in many domains, such as detecting fraudulent credit card transactions, insurance and tax fraud detection, intrusion detection for cyber security, failure detection, direct marketing, and medical diagnostics. Although anomalies are by definition infrequent, in many examples their importance is quite high compared to other events, making their detection extremely important. This tutorial will provide an overview of the research done in the increasingly important field of anomaly detection. The tutorial will cover the existing literature from a variety of perspectives, such as nature of input/output, and the availability of supervision. Anomalies will be divided into three broad groups: (i) Point anomalies, (ii) Contextual anomalies, and (iii) Structural anomalies, and a wide variety of anomaly detection methods appropriate for each type of anomaly will be presented. Additionally, the tutorial will discuss several application domains, such as intrusion detection, fraud detection, industrial damage detection, healthcare informatics, where anomaly detection plays a central role.