The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. Much progress has been made with mathematical and statistical aspects of forecasting models and related techniques, and experience has been gained through application in a variety of areas in commercial and industrial, scientific and socio-economic fields. Indeed much of the technical development has been driven by the needs of forecasting practitioners. There now exists a relatively complete statistical and mathematical framework that is described and illustrated here for the first time in book form, presenting our view of this approach to modelling and forecasting. The book provides a self-contained text for advanced university students and research workers in business, economic and scientific disciplines, and forecasting practitioners. The material covers mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each chapter. In order that the ideas and techniques of Bayesian forecasting be accessible to students, research workers and practitioners alike, the book includes a number of examples and case studies involving real data, generously illustrated using computer generated graphs. These examples provide issues of modelling, data analysis and forecasting.