I took a course in Complex Analysis last term and really enjoyed it. The level though was very basic, the last bit that we did was to prove the Cauchy Residue Theorem. We haven't even touched upon important aspects such as for example Analytic Continuation.
I'd love to take this further on my own, and I'm curious to know:
Which aspect, topic or concept from Complex Analysis do you think is the most important or interesting to know about.
I would be more interested in applications of concepts from Complex Analysis within pure mathematics, rather than applications to science, but all thoughts are helpful!
Also, in case you have a favourite book about Complex Analysis, please post it!