This text presents modern developments in time series analysis and focuses on their application to economic problems. The book first introduces the fundamental concept of a stationary time series and its relation to the basic properties of covariance funtions, investigating the structure and estimation of autoregressive-moving average (ARMA) models and their relations to the covariance structure. The book then moves on to non-stationary time series, highlighting its consequences for modeling and forecasting as well as regressions models and presenting standard statistical tests. Next, the text discusses volatility models and their applications in the analysis of financial market data, focusing on generalized autoregressive conditional heteroskedastic (GARCH) models. The second part of the text  is devoted to multivariate processes, such as vector autoregressive (VAR) models and structural vector autoregressive (SVAR) models, which have become the main tools in empirical macroeconomics. The text concludes with a discussion of co-integrated models and the Kalman Filter, which is being used with increasing frequency. The exposition finally connects to recent developments in the field. Mathematically rigorous, yet application-oriented, this self-contained text will help students develop a deeper understanding of theory and better command of the models that are vital to the field.  Assuming a basic knowledge of statistics and/or econometrics, this text is best suited for advanced undergraduate and beginning graduate students.