On the concept of IFSs -- Operations and relations over IFSs -- Geometrical interpretations of IFSs -- Modal and topological operators -- Extended modal operators -- Other types of operators -- Norms and metrics over IFSs -- Intuitionistic Fuzzy Relations (IFRs) -- New intuitionistic fuzzy operations -- On two new extensions of intuitionistic fuzzy sets -- Concluding remarks.;This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author ฬs previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author ฬs most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.