Abstract: The fundamental and simplest structure of a complex system is a network. According to this idea, we plan to develop a general methematical framework of complex systems. In this paper, we discuss in detail the concept of systems, a general description of systems: System=(Hardware, Software, Environment), and whole-part relations, including relations between elements and systems, subsystems and systems, and between systems. The rules of operations of systems are given, and the induced transformations between hardware and software of systems are briefly discussed.

Key words: complex systems, hardware, software, operations of systems, induced transformations, mathematical framework