This book offers the first systematic treatment of what is perhaps the most promising contender for a canonical inductive logic: objective Bayesian inductive logic. The book presents the logic in detail and sets out a range of novel results that demonstrate its conceptual and practical viability. Despite the fact that both deductive logic and standard inductive logics are undecidable, Bayesian networks can be used to draw inferences in the logic, with the potential for computational tractability. Beginning with the necessary theoretical background in inductive logic, the book goes on to define and motivate the objective Bayesian inductive logic and explore quantifier-free inferences as an important special case, demonstrating decidability and introducing Bayesian network inference methods. These results are then extended to a large class of quantified inferences, showing that the logic generalises Bayesian and Jeffrey conditionalisation and considering connections to belief revision. The text then concludes by developing further methods for drawing inferences in the logic, discussing ways in which the logic may be refined and posing some open questions for further research. Inductive Logic: A Bayesian Approach, is aimed at anyone with an interest in formal approaches to inference under uncertainty, including formal epistemologists as well as logicians working in philosophy, computer science or mathematics with a working knowledge of probability.This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations.