SummaryThis paper is an exposition of some elements of Wald's decision theory. Concepts like a priori distribution, decision function, loss function, risk, Bayes procedures, admissible procedures, minimax procedures, least favourable distribution are introduced all in connection with the problem of classification of observations into two given populations. The exact treatment of the procedures and their mutual relations are illustrated by numerical examples concerning univariate and multivariate normal populations. The extension towards the classification into more than two given populations concludes the paper.