(Topics in Complex Analysis II) Star-Shape and Laurent's Series

Based on the lecture of Prof. Pappalardi in the summer school about complex analysis, I wrote a complete note for my own on the topic about the Laurent's series. Via the proofs, we can see many corollaries, which are not mentioned in current note. If you are interested in complex analysis and related topics in algebraic geometry and number theory, the book of E. Freitag and R. Busam "Complex Analysis" is very useful. Because there are some figures that cannot be painted in the blog, I write all by hand, and I am very sorry about bad hand writing.