Preliminaries. General introduction. The reactive paradigm: its basic features. Natural and formal systems the concept of a natural system. The concept of a formal system. Encodings between natural and formal systems. The modelling relation. The modelling relation within mathematics. Specific encodings between natural and formal systems. Encodings of physical systems. Encodings of biological systems: preliminary remarks. Specific encodings of biological systems. Models, metaphors and abstractions. The encodings of time. Time and dynamics: introductory remarks. Time in Newtonian dynamics. Time in thermodynamics and statistical analysis. Probabilistic time. Time in general dynamical systems. Time and sequence: logical aspects of time. Similarity and time. Time and age. Open systems and the modelling relation general introduction. Open, closed and compensated systems. Compensation and decompensation. The main theorem. Models as closed systems. The concept of error. Error and complexity. Order and disorder. The stability of modelling relations. Anticipatory systems general introduction. An example: forward activation. General characteristics of temporal spanning. An application: senescence. Adaptation, natural selection and evolution. Learning. Selection in systems and subsystems. Perspectives for the future. Appendix. Index.