The principle of indifference is the heuristic idea that if we are equally ignorant about two statements, then we ought to assign them the same probability. The principle dates back to Laplace and the birth of mathematical probability. Although it is intuitively self-evident, it has a history of producing apparent paradoxes. It has no rigorous formulation in measure-theoretic probability theory. Hence, using measure theory alone, we are helpless to distinguish between valid and invalid uses of the principle. In this chapter, we give a precise formulation of the principle of indifference. We show that it is a natural generalization of a basic principle of deductive logic. We then give several examples of the principle of indifference in action. We begin with simple, discrete examples and progress to continuous examples in one and two dimensions. Our final example is the famous example of Bertrand’s paradox.