I've read Etingof's and then Fulton-Harris' books about the representation theory ("Intrdouction to representation theory" and "Representation theory. A first course" respectively) and found their subject very exciting!
Can someone, please, recommend me a textbook containing a kind of the "second course" in this branch of the mathematics? (It'd be great if someone recommended a "russian-style" book.)
(I heard a lot about the "Representation theory and complex geometry" written by Chriss and Ginzburg. Is it really so wonderful? And what other good references do you know?)
I'm going to learn the advanced representation theory for its own sake. But I'll be glad to see interesting intersections with the algebraic or complex geometry!
UPD: User Vincent's answer was really great! But it was only about the Lie groups. I'm also interested in such topics as Kac-Moody algebras, (double affine) Hecke algebras, category $\mathcal O$, Soergel (bi)modules, quantum groups and other things like those (maybe, quivers)… Can some of them be a part of the second (not third, fourth, etc.) course? And are there (less or more) introductory textbooks covering a part of this material?
Best Answer
The best textbook that covers a wide range of subjects is for me "A Tour of Representation Theory " by Lorenz. Of course it is close to a first course but I would say a little more advanced than the two books that you mentioned. Another similar one is "A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras" by Gruson and Serganova.
Here is a small collection in specific directions: