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This book presents an overview of the theory and applications of sequential methods for hypothesis testing and changepoint detection in a wide range of engineering and environmental domains. It describes all the important theoretical developments with an emphasis on applications, including environmental surveillance, biomedical engineering, image processing, computer security, econometrics, and finance. The text covers more practical discrete-time models as well as very general cases that include both continuous- and discrete-time models. In addition, it presents the results for multi-hypothesis tests and detection-isolation procedures.