Albert Gloden's book, Mehrgradige Gleichungen, was published in Groningen in 1944. Some of it is out of date, but it's still a good place to start the study of multigrade equations (equations in integers $$a_1^r+a_2^r+\cdots+a_n^r=b_1^r+b_2^r+\cdots+b_n^r$$ that hold for several values of $r$).