In this book the reviser Dr.M.D.Raisinghania added the latest papers of GATE, CSIR-UGC(NET) and latest questions of different Universities by making a separate appendix with the heading "MISCELLANEOUS RESULTS AND PROBLEMS BASED ON THE ENTIRE BOOK". Other important feature of the book is chapter-22 has been re-written and new useful results have been included in this chapter. Now the book is useful for Graduate students of Mathematics and Physics and the book is also useful for Post Graduate students of Mathematics. It is also useful for competition examinations like GATE, CSIR-UGC(NET) and various other competition examinations. This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.