Originally published in 1988, The Statistical Theory of Linear Systems deals with identification (in the sense of obtaining a model from data) of multi-input and multi-output linear systems, in particular systems in ARMAX and state space form. The book emphasizes the underlying theory. It covers:* Structure theory, in particular realization and parameterization of linear systems, with special emphasis on the analysis of properties of parameter spaces and parameterizations relevant for estimation and model selection.* Gaussian maximum likelihood estimation of the real-valued parameters of linear systems, with an emphasis on asymptotic theory* Model selection, in particular order estimation, by information criteria such as AIC or BIC, with an emphasis on asymptotic theory.* Procedures for calculation of estimates.* Approximation by rational functions.