Prediction error methods (PEM) represent a unified tool for parametric identification of linear dynamical systems. The key idea in PEM is to construct a predictor of the current output of a dynamical system based on past input and output observations. The optimal predictor is then computed by minimizing the power of the prediction error. In this seminar, the theory behind PEM will be presented, along with the numerical optimization algorithms needed for the implementation of prediction error methods. Analogy between PEM and other algorithms commonly used in system identification, such as linear least-squares, maximum likelihood estimation and simulation error minimization will be discussed.