I think the following references might be useful:
H. Weber (1895/1896): Lehrbuch der Algebra, 2 volumes. Vieweg, Braunschweig. If I remember correctly it includes exercises.
E. Artin (1938): Foundations of Galois Theory. New York University Lecture Notes, New York.
N. Bourbaki (1947): Éléments de Mathématique, Algèbre. Hermann, Paris.
I am not totally sure whether the last two references include exercises.