Spherical representation of extended complex plane, Analytic Functions, Harmonic Conjugates, Elementary Functions, Cauchy Theorem and Integral Formula, Homotopic version, Power Series, Analytic Continuation and Taylor's theorem, Zeros of Analytic functions, Hurwitz Theorem, Maximum Modulus Theorem and Open Mapping Theorem, Laurent's Theorem, Classification of singularities, Residue theorem and applications, Argument Principle, Theorems of Rouche and Gauss- Lucas, Mobius Transformations, Schwarz- Christoffel Transformation, Iterated Functions System, Fractals, Algorithms to generate Sierpinski Gasket.