Inductive Logic Programming is a young and rapidly growing field combining machine learning and logic programming. This self-contained tutorial is the first theoretical introduction to ILP; it provides the reader with a rigorous and sufficiently broad basis for future research in the area. In the first part, a thorough treatment of first-order logic, resolution-based theorem proving, and logic programming is given. The second part introduces the main concepts of ILP and systematically develops the most important results on model inference, inverse resolution, unfolding, refinement operators, least generalizations, and ways to deal with background knowledge. Furthermore, the authors give an overview of PAC learning results in ILP and of some of the most relevant implemented systems.