The aim of the course is to present some classes of probabilistic models of particular relevance in applications, in particular dynamic models. The emphasis is placed, in addition to mathematical rigor, on developing the ability to grasp the essential aspects of a real phenomenon and translate them into a model whose analysis, analytical or numerical, is accessible.The main topic of the course is the theory of Markov chains, both in discrete and continuous time. Each development of the theory is accompanied by the presentation of examples of applicative interest, motivated by economics, physical and biological sciences, but also by computational problems that emerge in the search for efficient algorithms. In the final part of the course the notions of conditional expectation and martingale will be introduced.At the end of the course, the student will have the tools to use a wide range of probabilistic models in both theoretical and applicative contexts, understanding their limits and effective applicability, also from a computational point of view. He will also be able to have a unifying and abstract vision of classes of problems with similar characteristics, and to face the reading of advanced texts.