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, appealing measures of complexity and distance for linear systems are defined and explicit numerical expressions are derived. A simple and new procedure for approximating a given system by one of less complexity is described. Finally, procedures and algorithms for deterministic time series analysis are presented. The procedures and algorithms are illustrated by simple examples and by numerical simulations.