I am taking a Galois Theory course using Cox's Galois Theory text book, and we have a required student project. Having read the section on Abelian Equations, section 6.5 page 143, I want to know more about them. Unfortunately, I can't find any resources for further reading using google or my college's library search. Do Abelian Equations go by a different name now, or is there not much interesting theory to follow up the book's presentation? Are there any links or books I can follow up with? Thanks.
The book ends its short section on Abelian Equations with the statement of the Kronecker–Weber theorem. The natural follow up from this point is Class field theory, which studies abelian extensions. An excellent introduction is the book Primes of the Form $x^2+ny^2$, also by Cox. See also the question Learning roadmap for Class Field Theory and more.