The book sets out to provide new methods and techniques for computer modelling of high complexity systems. Development of simulation and control techniques, and of problem-solving applications, is the aim. The discussed methods/techniques are called mathematicalheuristic methods, to enter the category of hybrid methods. The mathematical-heuristic model for simulation and control is composed of several models, of different kinds, i.e. a continuous and/or a discrete-time model, a discrete-event model, and a heuristic knowledge-based model and/or a fuzzy knowledge-based control model. The compatibility of models is ensured by two theorems of compatibility between mathematical, heuristic or fuzzy models. The author has developed an algorithm for simulation and control of high complexity systems based on a mathematical-heuristic model.