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(Von Neumann) regular rings have been studied since 1936. The central focus of the book is the study of some versions and generalizations of regular rings. The book has four chapters. The first chapter of the book has preliminary definitions and results. The second chapter comprises of extensive study of regular rings, weakly regular rings, strongly regular rings and unit regular rings. In this chapter, regular rings are also studied via some generalized injectivity properties of some classes of modules over them. The third chapter is devoted to the properties of flat modules. The fourth chapter of the book presents a survey of the von Neumann regularity of SF-rings between 1975-2009.