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I'm a PhD student and I would like learn about cluster algebras. I'm wondering what is a good reference (i.e., has detailed explanations, examples, etc) to learn from the basic and what are some of the different directions of research that's happening in this topic?

My background is related to representation theory of finite dimensional algebras.

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    $\begingroup$ What about arxiv.org/abs/1608.05735 and arxiv.org/abs/1707.07190? $\endgroup$
    – Richard Stanley
    Commented Dec 21, 2022 at 0:40
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    $\begingroup$ @RichardStanley's suggestion would be my number one too. On current research topics, can you go to a grad workshop (sometimes called summer school, winter school etc.)? There's usually one or two a year on cluster algebras; look on the FDList. And several from the past couple of years were recorded when given online, so you might find some of these. Oh, and ask more MO questions - quite a lot of that community is here and happy to help 😊 $\endgroup$
    – Jan Grabowski
    Commented Dec 21, 2022 at 11:07
  • $\begingroup$ Name of @RichardStanley's suggestion: Fomin, Williams, and Zelevinsky - Introduction to Cluster Algebras, Chapters 1–3 and 4–5. $\endgroup$
    – LSpice
    Commented Dec 22, 2022 at 19:51
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    $\begingroup$ You might also consider Pavel Galashin's course which has recorded lectures on YouTube and lecture notes: math.ucla.edu/~galashin/206B_2021_cluster_alg.html $\endgroup$
    – Igor Pak
    Commented Dec 26, 2022 at 20:04

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