I want to start stuyding complex analysis on a graduate level on my own (self study). I'm having trouble with diciding which one of the following books to use:

  • Serge Lang's Complex Analysis or
  • John. B. Conway's Functions of One Complex Variable.

Here's the first part of the contents of both books:

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As you can see, Conway has a chapter on Metric Spaces and the Topology of $\Bbb C$, and starts with power series in the third chapter, while Lang does it directly in the second chapter.

Which of these two books do you guys recommend me and why?

  • $\begingroup$ I don't know if my recommendation will be useful for you but when I took Complex Analysis I followed a book called Basic Complex Analysis by Marsden and Hoffman. The book is beautiful and have a lot of examples and exercises of various levels. About the books that you are considering, I prefer Conway's book. In fact, you can follow Conway and complement it with Marsden. $\endgroup$ – Carlos Jiménez Jun 29 '18 at 4:41
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    $\begingroup$ For self-study, Conway’s textbook is better since it has more explanations assuming only single variable calculus as opposed to Lang’s textbook $\endgroup$ – user555729 Jun 29 '18 at 6:28
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    $\begingroup$ Lang is a good book, but I would advise you to use Conway or Ahlfors (my personal choice) if you're learning it for the first time. $\endgroup$ – Brian Moehring Aug 11 '19 at 1:29

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