This chapter describes the logic of inductive inference as seen through the eyes of the modern theory of personal probability, including a number of its recent refinements and extensions. The structure of the chapter is as follows. After a brief discussion of mathematical probability, to establish notation and terminology, it recounts the gradual evolution of the probabilistic explication of induction from Bayes to the present. The focus is not in this history per se, but in its use to highlight the (...) key assumptions, criticisms, refinements, and achievements of that theory. Along the way, the structure of the modern theory is presented, and its relation to the problem of induction discussed. (shrink)