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This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition. Set Theory Real numbers Sets in R Real functions Sequence Series Limits Continuity Differentiation Functions of bounded variation Riemann integral Improper integrals Sequence of functions Series of functions Power series APPENDIX 1- Sets in R2 APPENDIX 2- Sequence in R2 ANSWERS TO EXERCISES BIBLIOGRAPHY INDEX