What shall I learn in order to understand Auslander-Reiten theory and tilting theory? I work on cluster algebras and quivers and hence I need to understand Auslander-Reiten theory and tilting theory as soon as possible. I have read some noncommutative algebra and homological algebra but still have trouble pondering on Auslander-Reiten-Smalo's book, Representation Theory of Artin Algebras. Without Auslander-Reiten theory I can not understand tilting theory, either. May I ask what shall I learn in order to understand both of them? Thank you very much!

I'd recommend the book _Elements of the Representation Theorey of Associative Algebras_ by Assem, Simson, & Skowroński. It covers both Auslander-Rieten Theory, Tilting Theory, and almost all of the background required to understand those chapters.