It is well-known that physical FASs are a perfect type of systems in the sense that their controllers can be easily designed and the resulted closed-loop systems can often be made globally constant linear. If, by any chance, every system could be converted into a FAS, then the control designs of all dynamical systems would be systematically and well solved. However, under physical restrictions, this goal is not practical and in general not achievable. Fortunately, a recent significant achievement on the discovery of the mathematically generalized FAS models of dynamical systems made an important milestone toward this goal. Namely, although a non-FAS cannot be converted into a physical FAS, it can be converted into a mathematically generalized FAS. Moreover, like a physical FAS, the control of a mathematically generalized FAS can also be easily realized. Such facts and logic naturally motivate the so-called FAS approach that solves control systems design based on generalized FAS models. In this Introduction Chapter, the birth backgrounds of the FAS approach and its difference from the well-known state-space approach are briefly stated. Recent developments of the FAS approach are overviewed. The contents of the book are previewed, and some commonly used symbols and preliminary technical results are also presented.