Qualifications to tutor Abstract Algebra
I've tutored Abstract Algebra at least 10 times now, covering topics in Group Theory, cyclic groups, normal subgroups, homomorphisms, the isomorphism theorems, orbit-stabilizer theorem, Polya counting and the class equation, Sylow's theorems, rings, fields, modules, integral domains, unique factorization domains, principal ideal domains, ideals, rings of polynomials, the Chinese Remainder Theorem, and reducibility.
I am familiar primarily with Dummit and Foote's textbook, as well as some sections from Artin, Fraleigh, and Herstein.