This book collects notes that were prepared for a university course taught in the Spring of 2018, and delivered to an audience of students enrolled in the Master course in Logic, philosophy and history of science of the University of Florence. The goal of the course was to introduce students to some basic concepts from the area of research generally known as decision theory. This is done by focussing on the concept of 'rational choice', which is analyzed, methodologically speaking, by the means of the theory of games. To minimize prerequisites it was decided to restrict the attention to the theory of finite games in particular. The topics treated are vary, and belongs to both the theory of games 'in normal form' as well as that of games 'in extensive form', as they are usually referred to. The classical issues in both fields, such as the theory of 'equilibria' and the study of properties such as determinacy, are carefully discussed to make them clear to beginners and are addressed from a novel perspective which makes use of formal methods that are typical of researches connected with the study of logic.