This text introduces the reader to basic concepts and techniques in the field of fuzzy sets and gives an account of the literature. It does not treat applications, but rather provides a theoretical foundation for applying fuzzy set theory. The main topics which are treated are: basic set theory, basic lattice theory, operations on fuzzy sets, t-norms and t-conorms, special types of fuzzy sets, fuzzy relations, functions working on fuzzy sets, fuzzy real numbers (both probabilistic and non-probabilistic), basic classical logic and fundamentals concerning fuzzy logic. This volume is intended for researchers working in the areas of engineering, data analysis, control theory, pattern recognition, neural networks, clustering, expert systems, information retrieval, operations research, decision-making, image and signal processing, and for those who require more information on the set-theoretical basics on which fuzzy set theory is founded.