Publisher Summary This chapter focuses on the classical stability that motivates the continuing concern with control theory that is observed in the engineering and mathematical journals. One of the basic objectives of science is to predict the future. This clairvoyance may range from that of the date of the next eclipse, earthquake, or recession, to that of the failure of a structure such as a building or bridge under sustained vibration. The crystal ball of science is the classical descriptive approach, aided and amplified by mathematical ingenuity and the electronic computer. Systems cannot be described in a compact fashion and many further state variables may be required and more complicated functional relations requiring the past history of the system may be necessary. One of the most interesting and important qualitative properties of a solution are that of stability. This means the ability of the solution of the equation to preserve certain structural features under various types of changes in the values of the initial conditions, or the form of the equation, or both.