The book contains the transcription of a course on the foundations of probability given by the Italian mathematician Bruno de Finetti in 1979 at the National Institute of Advanced Mathematics in Rome. Bruno de Finetti (1906-1985) is known worldwide as the founder (together with F.P. Ramsey) of the modern personal probability. His fundamental idea of coherence, along with his Dutch Book argument, continues to play a central role in the debates about the foundations of probability and decision theory. Moreover, his notion of exchangeability and the related Representation Theorem are at the heart of the modern Bayesianism in statistics and epistemology. Unlike the hard-to-read two-volumes major work Theory of Probability (1970) (translated into English and published in 1974 by Wiley), this book is accessible to a wide audience, being conducted at a very elementary mathematical level, with no sacrifice of conceptual rigour. This book provides a fresh and first-hand introduction to De Finettis personalistic standpoint. Although primarily meant as an introduction, the book should interest also scientists and philosophers well acquainted with De Finettis views. As a matter of fact, the book contains the last reflections by De Finetti that include important conceptual novelties and new answers to common objections. The editor added a new introductory essay (replaces the paper in the original Italian edition), a rich apparatus of explicative notes and an updated bibliography. A further new preface by Maria Carla Galavotti is added to this English edition.