Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this text is twofold: firstly, to point out present gaps in the way data fusion problems are conceptually treated, and secondly, to address this issue by exhibiting mathematical tools which treat a combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two ideas relating to probability theory: the newly developed fields of random set theory and conditional and relational event algebra. The book is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional and relational event algebra. The text may be useful as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.