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The book addresses its content to control and systems science and engineering professors, researchers, Ph. D. and graduate students, designers, as well as to applied mathematicians and researchers and engineers dealing with dynamics and linear mathematical modeling of technical plants and processes. The primary purpose of control is to force the behavior in an unpredictable environment (under the actions of unknown and possibly immeasurable disturbances and unpredictable, hence most probably non-zero, initial conditions). This means that a kind of tracking is the key property that should characterize the control system. Surprisingly, the tracking theory has not been well developed. It is the stability theory that has been dominating. However, stability and tracking are mutually independent. The book sets up the fundamentals of the tracking theory for the control systems. Various tracking properties defined in the book express different tracking qualities.