Question for recommending a good textbook in representation of quivers I am taking representation of quivers, and the lecture notes seems not enough. So could you recommend a good textbook for this course. There is a new book "Quiver Representations, by  Ralf Schiffler" costing more than $60, and I don't know whether it is worth or not. So could you recommend a good textbook for this course?
Thanks,
 A: I suggest the following:
Ringel, Schröer: Representation Theory of Algebras I: Modules
(https://www.math.uni-bielefeld.de/~ringel/opus/dst1.pdf)
Ringel, Schröer: Representation Theory of Algebras II: Auslander-Reiten Theory
https://www.math.uni-bielefeld.de/~ringel/opus/dst2.pdf
Krause: Representations of Quivers via reflection functors
http://www2.math.uni-paderborn.de/fileadmin/Mathematik/AG-Krause/publications_krause/quiver.pdf
The first two don't focus on quivers, but still have a good bit on it. The third one deals with quivers and how to find their representations only. I found these sources to complement each other well.
Still I'm hoping for an actual book on that topic to be released sometime...
A: I haven't had a look at Schiffler's new book, so I can't judge, but here are some alternatives:
Assem-Simson-Skowronski: Elements of the representation theory of the representation theory of finite dimensional algebras (Parts 1-3), Part 1 is enough for basic purposes. Is quite combinatorial, uses many examples from representation theory of quivers, uses right modules. (covers AR theory)
Auslander-Reiten-Smalo: Representation theory of Artin algebras. More abstract than the other book, also has more of the theory of group algebras and selfinjective algebras. (covers AR theory)
Benson: Representations and Cohomology I+II. Not aiming at quiver representations, but also has something about quivers in it. Quite dense, not aimed at the student starting to learn representation theory, but a good survey over many topics. (covers AR theory)
Etingof et. al.: Introduction to representation theory: Much shorter than the others, interesting in that it covers quiver representations as well as representations of Lie algebras, and group algebras. That's why not much is covered in each of these topics. Also available online. (does not cover AR theory)
Ringel, Schröer: Representations of finite dimensional algebras. A preprint of a book, that was available online for some time, and from reading the abstract of Schiffler's book, seems to cover roughly the same topics. Not able to find it anymore at the moment, might appear again, or in print in the future. (covers AR theory)
Brion: Representations of quivers. Lecture Notes introducing quiver representations, focussing towards geometric aspects. Available from the author's webpage.
Crawley-Boevey: (More) representations of quivers. Lecture Notes introducing quiver representations, also focussing towards geometric aspects. Available from the author's webpage.
