This book presents the rudiments of fuzzy set theory and fuzzy logic and related topics and their applications in a simple and easy-to-understand manner. Written with a general type of reader in mind, the book avoids the extremes of abstract mathematical proofs as well as specialized technical details of different areas of application. The book is intended to motivate the readers in getting a clear grasp of the basic concepts of the subject and its possible applications. A special feature of the book is that the exercises at the end of each chapter are preceded by a set of short-answer review-type questions. These are intended to help the reader in developing the confidence that he/she has correctly grasped the concepts introduced in the chapter. The book can be used as a text for the study of the topics of fuzzy set theory, fuzzy logic and their possible applications at the undergraduate, graduate and postgraduate students of mathematics, engineering and other disciplines of science, arts and medicine. In this book: Introduction Fuzzy Sets Operations on Fuzzy Sets Fuzzy Numbers Fuzzy Relations and Fuzzy Graphs Fuzzy Functions and Calculus of Fuzzy Functions Measures of Vagueness and Uncertainty Evidence Theory, Possibility Theory and Probability Theory Linguistic Variables, Fuzzy Rules and Fuzzy Propositions Fuzzy Logic and Approximate Reasoning Decision Making in a Fuzzy Environment Construction of Fuzzy Sets and Defuzzification Fuzzy Rules Based Models and Fuzzy Systems Engineering and Other Applications Intutionistic Fuzzy Sets, Rough Sets, Vague Sets and Soft Sets