This book entitled "INTRODUCTION OF REAL ANALYSIS VOLUME-1” is consists of Ten chapters. In chapter 1, we have discussed real number system which includes basic properties of real number system as well as binary expansion etc. In Chapters 2 covers the introduction and properties of open and closed sets, limit points etc. In Chapters 3 deals infinite sets and countable sets. While Chapters 4 concerns the sequences, basic properties and some important definition and theorems. In Chapters 5, we have discussed Limit and Continuity of Functions, basic properties and some important definition and theorems. In Chapters 6, we have to study the Limit and Continuity of Function, some important definition and theorems. In Chapters 7 covers the introduction of Functions of Several Variables, some important definition and theorems. In Chapters 8 deals the introduction of Riemann Integral, some important definition, theorems and examples. In Chapters 9, we have discussed, the introduction of Uniform Convergence, some important definition, theorems and examples. In Chapters 10 deals the introduction and properties of Improper Integrals. Also at the end of every chapter, multiple objective questions are discussed.
