In deterministic identification the identified system is determined on the basis of a complexity measure of models and a misfit measure of models with respect to data. The choice of these measures and corresponding notions of optimality depend on the objectives of modelling. In this monograph, the cases of exact modelling, model reduction and approximate modelling are investigated. For the case of exact modelling a procedure is presented which is inspired by objectives of simplicity and corroboration. This procedure also gives a new solution for the partial realization problem. Further,...