This book presents a new method for the diagnosis and observation of dynamical systems. This approach is presented with a strong theoretical background. The given methods are developed for engineering applications and are illustrated with numerous graphic and practical examples. In the first part of the book, new results in the area of automata theory, such as the solution to supervision problems for stochastic automata, are presented as well as an elaborated study on automata networks. The second part presents a new approach to qualitative modelling of dynamical systems based on quantized systems. This methodology opens the path towards application and is described and illustrated in detail. In conclusion practical applications of the developed methods are demonstrated.