The initiation of the study of generalized closed set was done by N Levine in 1970 . Later on N Palaniappan introduced the concept of Regular Generalized closed set in 1993.Lots of work has been done by many Researchers in National and International level in this field . Some of my papers are also published in various Journals . The main objectives of the proposed book are to generalize the concept of regular open sets. To construct some stronger and weaker forms of generalized regular open sets . Also the concepts of regular dense sets and regular rare sets are introduced.To study the topological space formed by the collection of the above sets .To study the relationship between the various sets obtained above and also between the corresponding topological space. To study some new separation axioms which may help much in dealing with digital topology.Lastly the application of the above sets and the topological spaces are shown.This book may help a lot to the Researchers working in the field of ordinary Topology and fuzzy topology. Not only the Researchers but this book may also help the P.G students of Various Universities having Topology or Fuzzy Topology as Special paper.