This book provides an exploration of the role of mathematical logic in randomness, probability, complexity, learning theory, dynamical systems, computability, and set theory. In a self-contained text that uses a common language, Calvert explains how logic informs these topics so that researchers can see the connections between them that might otherwise not be appreciated. He shows how probability logics not only have a role to play in the individual development of each of these areas, but also are a unifying force, bringing them together to promote further advances. Thoroughly referenced and engagingly written, this is a thought-provoking resource for graduates and researchers across multiple disciplines.