The author presents the main topics of statistical inference and two - decisions problems formulated in terms of testing hypotheses using the concept of likelihood. Various optimum properties of the maximum likelihood estimates of the parameters of the statistical models have been shown and proved in the linear and generalized linear models. For these purposes the most important and necessary statistical backgrounds are presented in the volume or in the appendix. The maximum likelihood method is introduced by several examples. A unified theory of linear models is presented. The generalized linear models appeared as a natural extention of the former and are motivated from scientifique, technological and economical points of view. All six chapters and the appendix are illustrated with relevant applications and exercises.