iability, Analycity, Cauchy-Riemann Equations. 3. Power Series and derivitives. 4. Complex Log, Exponential and Trig functions. 5. Complex Integration, Cauchy theorem, Cauchy Integral Formulae. 6. Taylor Series, Laurent Series and Residues. 7. Mobius Tranformations. This is not the whole of Complex Number theory since there is always more. But the content here is for those who are interested and want to develop a deeper understanding of the subject. For those having this as a course, hopefully this will help since this is a pretty high level course requiring a good understanding of mathematics and concepts from real analysis at the start.