Since the publication of the first edition of this highly regarded textbook, the value of data assimilation has become widely recognized across the Earth sciences and beyond. Data assimilation methods are now being applied to many areas of prediction and forecasting, including extreme weather events, wildfires, infectious disease epidemics, and economic modeling. This second edition provides a broad introduction to applications across the Earth systems and coupled Earth-human systems, with an expanded range of topics covering the latest developments of variational, ensemble, and hybrid data assimilation methods. New toy models and intermediate-complexity atmospheric general circulation models provide hands-on engagement with key concepts in numerical weather prediction, data assimilation, and predictability. The inclusion of computational projects, exercises, lecture notes, teaching slides, and sample exams makes this textbook an indispensable and practical resource for advanced undergraduate and graduate students, researchers, and practitioners who work in weather forecasting and climate prediction.