This book provides a complete round-up of developments concerned with the application of partial moments in system identification and data-driven modelling; it captures the essence of work carried out at the Laboratoire d'Informatique et d'Automatique pour les Systèmes for more than 40 years.   The book begins with introductory material, describing both the mathematical tools associated with partial moments and reinitialized partial moments and an example demonstrating their use. The authors then proceed to show how these tools can be used for the identification of continuous-time linear models, discrete-time linear models, continuous-time linear state-space models, linear parameter-varying models and multidimensional models based on partial differential equations. The properties and performances of each of these approaches are presented. The analogy with algebraic approaches is proved, thus opening perspectives for extension to other fields. The text removes some long-standing limitations on the implementation of partial-moment-based tools in system identification.   This book is of interest to researchers and postgraduates studying system identification, control theory, applied mathematics and computer science. It is also useful for engineers working on industrial applications of the parametric estimation of mathematical models.