Abstract Algebra

As far as the canonical texts of math goes, Dummit and Foote is excellent. I'm also fond of the first half of Munkres' Topology.

Dummit & Foote is fantastic for algebra. I also really liked Carrothers for analysis. None of the other books I used really stood out, other than Lang's algebra book, but that one was for the opposite reason - once, he said "the following is obvious" and I thought, "oh yes, it is!" and it was one of my proudest moments as a math student. Would not recommend for self-teaching. More important than a good teacher, imo, is collaborators you're learning with who are around your same level. Sometimes they should figure out exercises faster than you, sometimes you should figure things out faster than them, often together. If that's not happening, it's a lot harder (and more frustrating) to learn. This becomes more important the more advanced you get. I never found lectures useful really but if I had no one to collaborate with I was almost certainly going to drop the class.

Personally I have heard nothing but bad things about Artin. Most people I know recommend Dummit and Foote instead; its increase in difficulty is supposedly offset by superior presentation of the material.