A principal feature of this book is the substantial care and attention devoted to explaining the basic ideas of the subject. Whenever a new theoretical concept is introduced it is carefully explained by reference to practical examples drawn mainly from the physical sciences. Subjects covered include: spectral analysis which is closely intertwined with the "time domain" approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data. The inclusion of material on "kalman filtering," state-space filtering," "non-linear models" and continuous time" models completes the impressive list of unique and detailed features which will give this book a prominent position among related literature. The first section -- Volume 1 -- deals with single (univariate) series, while the second -- Volume 2 -- treats the analysis of several (multivariate) series and the problems of prediction, forecasting and control.