Time Series Modelling with Unobserved Components provides a comprehensive introduction to the Unobserved Components Model (UCM) approach for analysing and forecasting time series data. Written by Matteo M. Pelagatti, the book bridges statistical theory and practical application, making advanced state-space modelling techniques accessible to students, researchers, economists, and data analysts. The book begins with the fundamentals of statistical prediction and classical time series concepts, including stationarity, ARIMA models, and forecasting principles. It then develops the UCM framework by explaining how observed time series can be decomposed into underlying components such as trend, seasonal variation, cyclical movements, and irregular fluctuations. The text introduces the state-space representation of these models and explains estimation using the Kalman filter and smoothing algorithms. The later chapters focus on practical modelling strategies, intervention analysis, regression with time-varying coefficients, missing observations, outlier detection, and real-world applications such as business cycle analysis and economic forecasting. The author also reviews statistical software packages that support UCM estimation, enabling readers to implement these techniques in practice. The book is especially valuable for postgraduate students and professionals in statistics, econometrics, finance, economics, engineering, and data science.