Author of a monograph on one of the most important medieval law professors, Huguccio. The Life, Works, and Thought of a Twelfth-Century Jurist (CUA Press, 1994) and a book (in German) on the criminalization of abortion in the late medieval West, Die Abtreibung. Anfänge der Kriminalisierung, 1140-1650. (Cologne, Weimar, and Vienna: Boehlau, 2000). He is co-editor (with Ludwig Schmugge) of volumes 3 and 5 (Tübingen: Niemeyer, 2000, 2002) of the Repertorium Poenitentiaria Germanicum, cataloguing entries relating to German recipients in the records of the Apostolic Court of Penance under Calixt III (1455-58) and Paul II (1464-1471). Dr. Mueller has also published numerous articles in German, Italian, and American journals on late medieval scientific law, its application in the courts, and papal administration.  

In addition to medieval survey classes, he is teaching undergraduate and graduate courses on religion, family, and society, as well as seminars examining legal and institutional developments of the period.