Formal methods are changing how epistemology is being studied and understood. A Critical Introduction to Formal Epistemology introduces the types of formal theories being used and explains how they are shaping the subject. Beginning with the basics of probability and Bayesianism, it shows how representing degrees of belief using probabilities informs central debates in epistemology. As well as discussing induction, the paradox of confirmation and the main challenges to Bayesianism, this comprehensive overview covers objective chance, peer disagreement, the concept of full belief, and the traditional problems of justification and knowledge.