This book provides a unified and comprehensive presentation of the theory and models underlying time series analysis. The focus is on the weakly stationary case and linear models: the first part derives the theory of general multivariate weakly stationary processes in both time and frequency domains, including their forecasting and filtering. The second part deals with multivariate AR, ARMA, and state-space systems as the most important model classes for stationary processes. In this context, Yule-Walker equations, the factorization of rational spectra, the Kalman filter, and the structure of ARMA and state-space systems are described. The aim of the book is to present the essential concepts, ideas, methods, and results in a mathematically rigorous form, thereby providing a solid foundation for students and researchers.