The book presents the state-of-the-art of the mathematics in fuzzy logic and some related topics as seen by prominent researchers in this area. It covers the most important areas such as the structure of truth values, consequence operation, fuzzy relations, functional representation, extensions to other areas of logic, as well as some critical expositions on the essence of membership degrees or fuzzy measures and t-norms. The book contains many new results which are published for the first time.