Fuzzy Sets -- The Operation of Fuzzy Set -- Fuzzy Relation and Composition -- Fuzzy Graph and Relation -- Fuzzy Number -- Fuzzy Function -- Probabilisy and Uncertainty -- Fuzzy Logic -- Fuzzy Inference -- Fuzzy Control and Fuzzy Expert Systems -- Fusion of Fuzzy System and Neural Networks -- Fusion of Fuzzy Systems and Genetic Algorithms.This basic textbook gives an easily accessible introduction to Fuzzy theory and its applications. It provides basic and concrete concepts of the field in a self-contained, condensed and understandable style. This "First Course on Fuzzy Theory and Applications" includes numerous examples, descriptive illustrations and figures of the basic concepts, as well as exercises at the end of each chapter. The author has long time experience in teaching on fuzzy theory and its applications and continuously developed and summarized his didactic lecture notes into this book. This book can be used in introductory graduate and undergraduate courses in Fuzziness and Soft Computing and is recommendable to students, scientists, engineers, or professionals in the field for self-study.