Based on the assumption that all mathematics can be built up from sets, one has to first define fuzzy sets and their variations. This chapter explores truth values and their algebras and presents basic ideas and results of lattice theory. In 1965, Zadeh published a paper entitled “Fuzzy Sets” where he introduced his fuzzy sets. In classical set theory, one can define a set using the list method or the rule method. Two very important concepts of fuzzy set theory, which have been introduced by Zadeh, are the concepts of an alpha-cut and of a strong alpha-cut. An alpha-cut is a crisp set that consists of those elements that have membership degree greater than or equal to a specific value. The chapter provides a discussion on triangular norms or t-norms and triangular conorms or t-conorms. It also describes L-fuzzy sets and intuitionistic fuzzy sets.