1. Introduction.- 1.1 Essence of fuzzy set theory.- 1.2 Development of fuzzy set theory.- 2. Basic Notions of Fuzzy Set Theory.- 2.1 Fuzzy sets.- 2.2 Characteristic parameters (indices) of a fuzzy set.- 2.3 Linguistic modifiers of fuzzy sets.- 2.4 Types of membership functions of fuzzy sets.- 2.5 Type 2 fuzzy sets.- 2.6 Fuzziness and probability: two kinds of uncertainty.- 3. Arithmetic of Fuzzy Sets.- 3.1 The extension principle.- 3.2 Addition of fuzzy numbers.- 3.3 Subtraction of fuzzy numbers.- 3.4 Multiplication of fuzzy numbers.- 3.5 Division of fuzzy numbers.- 3.6 Peculiarities of fuzzy numbers.- 3.7 Differences between fuzzy numbers and linguistic values.- 4. Mathematics of Fuzzy Sets.- 4.1 Basic operations on fuzzy sets.- 4.2 Fuzzy relations.- 4.3 Implication.- 5. Fuzzy Models.- 5.1 Structure, main elements and operations in fuzzy models.- 5.2 Significant features of rules, rule bases and fuzzy models.- 5.3 Advice relating to rule base construction.- 5.4 Reduction of the rule base.- 5.5 Normalization (scaling) of the fuzzy model inputs and output.- 5.6 Extrapolation in fuzzy models.- 5.7 Types of fuzzy models.- 6. Methods of Fuzzy Modeling.- 6.1 Fuzzy modeling based on the system expert’s knowledge.- 6.2 Creation of fuzzy, self-tuning models based on input/output measurement data of the system.- 6.3 Creation of self-organizing and self-tuning fuzzy models based on input/output measurement data of the system.- 7. Fuzzy Control.- 7.1 Static fuzzy controllers.- 7.2 Dynamic fuzzy controllers.- 7.3 The determination of structures and parameters for fuzzy controllers (organization and tuning).- 8. The Stability of Fuzzy Control Systems.- 8.1 The stability of fuzzy control systems with unknown models of plants.- 8.2 The circle stability criterion.- 8.3 The application of hyperstability theory to analysis of fuzzysystem stability.- References.