This paper discusses a formulation of a basic theory of the information systems, where information is not only transmitted, but is also processed and memorized during the transmission. A deterministic procedure applied by an information system is defined as a logical work, and two measurements with information X, information quantity I(X) and information vitality T(X), are introduced. A system with the ability of transmitting, processing and memorizing information is called an information engine. A system of interconnected information engines is called an information network. The power of an information engine is defined as the maximum capacity of the logical works performed by the engine, and important properties of total power of information network are derived. Response time characteristics and cost minimizing problems of an information network are also discussed.