Donald Sarason's "Complex Function Theory". There are bigger more complete books on complex analysis. There are even ones that are more appealing, like "Visual Complex Functions" by Elias Wegert. Sarason's book is only 160 pages long, with legible text and clear examples. It covers the length of an undergraduate university class, and explains Holomorphic functions perfectly. The proofs are crystal clear, and so are the motivations. I haven't seen a better introduction.
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