This chapter introduces the basic concepts, notation, and basic operations for fuzzy sets. It describes linguistic variables and linguistic values and explains how to use them in fuzzy rules, which are an efficient tool for quantitative modelling of words or sentences in a natural or artificial language. The chapter describes different schemes of fuzzy reasoning, where inference procedures based on the concept of the compositional rule of inference are used to derive conclusions from a set of fuzzy rules and known facts. Fuzzy rules and fuzzy reasoning are the basic components of fuzzy inference systems, which are the most important modelling tool based on fuzzy set theory. The “fuzzy inference system” is a popular computing framework based on the concepts of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. The chapter presents the main ideas underlying fuzzy logic and points out the many possible applications of the powerful computational theory.