The scope of this paper is to discuss the safety and stability of the Internet System by use of knowledge from the Theory of Systems. This is achieved by: (a) reviewing fundamental knowledge of the Theory of Systems in order to apply it to the Internet system; (b) applying this knowledge in the case of the Internet; (c) discussing the safety and stability of the Internet System by use of the above-mentioned knowledge. By this approach we show that: a) The Internet is a system only if it operates under rules. b) The Internet is a global system, which means that is a system without environment and as such is subject only to Internal disturbances, which can very easily render it unstable. c) The Internet System can be secure only by implementing rules, which prohibit anonymity of users and force all to work in synergy for the achievement of a common scope, which is communication and diffusion of information and knowledge and d) The Internet System can be safe only by close monitoring its operation and by intervening to prevent the application of destabilizing disturbances by any of its elements.