Program synthesis is a solution to the software crisis. If we had a program that develops correct programs from specifications, then program validation and maintenance would disappear from the software life-cycle, and one could focus on the more creative tasks of specification elaboration, validation, and maintenance, because replay of program development would be less costly. This monograph describes a novel approach to Inductive Logic Programming (ILP), which cross-fertilizes logic programming and machine learning. Aiming at the synthesis of recursive logic programs only, and this from incomplete information, we take a software engineering approach that is more appropriate than a pure artificial intelligence approach. This book is suitable as a secondary text for graduate level courses in software engineering and artificial intelligence, and as a reference for practitioners of program synthesis.