Table of Contents: section br>i1 Riemann Integration2. Improper Integrals3. Integral as a function of a parametersection II4. Series of arbitrary Terms5. Double Series6. Fourier Series7. Differentiability of functions of two variablessection III8. Stereographic projection of complex Numbers9. Functions of a complex Variable10. Elementary Functions11. Conformal mappingsection IV12.Metric spaces13.Bases, sub-bases and Subspaces14.Convergence of sequences of metric spaces15.Completeness16.Isometry and Contraction17.Continuity and Homeomorphism18.Compactness and connectedness19.Construction of real numbers as the completion of the in complete examination Paper.