Henri Poincare, the French mathematician, physicist, and philosopher said that "if this calculus be condemned, then the whole of the sciences must also be condemned." Indeed, the concept of probability plays a crucial role in modern science and contemporary philosophy. While there is a broad consensus about the formal theory of probability, there is no agreement on its interpretation. In the course, we shall first look at the history of probability until the 19th century, then study the main contemporary interpretations of probability and finally consider some applications of these interpretations in science and/or philosophy. The course will be taught as a seminar in which students present the main readings and some of the further readings.