An essential competence of a skilled engineer is the ability to build mathematical models of components, equipment, machines and whole systems. Such models will be used to simulate their dynamical behaviour or to design control algorithms, to detect failures, to filter, interpolate and forecast future evolution; in short, models can be used to support decisions in complex situations or give advice in scenario evaluations.This textbook is addressed to the students of the first year of the Master Degree in Mechatronics Engineering - or to those following a similar curriculum in the automation and control fields -, with the aim of introducing the Lagrangian approach to the modelling of mechanical, electrical and electromechanical components, which are commonly found in a number of mechatronic systems.After an introduction to the use of vectors and matrices for the description of rigid bodies motion, the fundamental concept of energy is presented, as the Lagrangian approach requires the definition of both kinetic and potential energies and co-energies.