Giger's research interest have concentrated on nineteenth-century Italian opera and the work of Leonard Bernstein. He is the author of the monograph Verismo (Wiesbaden: Steiner, 2004) in the Handwörterbuch der musikalischen Terminologie and the book Verdi and the French Aesthetic: Verse, Stanza, and Melody in Nineteenth-Century Opera (Cambridge University Press, 2008), which was supported by a grant from the National Endowment for the Humanities. In addition, he is the author of articles in many books and journals, including the Journal of the American Musicological Society, The Journal of Musicology, the Cambridge Opera Journal, the Cambridge Companion to Verdi, Acta musicologica, Music & Letters, the International Review of the Aesthetics and Sociology of Music, and the second edition of the New Grove Dictionary of Music and Musicians, among others. He is currently preparing the critical edition of I due Foscari for The Works of Giuseppe Verdi.
Giger has co-edited (with Thomas J. Mathiesen) Music in the Mirror: Reflections on the History of Music Theory and Literature for the 21st Century (University of Nebraska Press, 2000), for which he has received an ASCAP Deems-Taylor award. He is also the founder of the Internet database saggi musicali italiani on Italian music theory and aesthetics, a Thomson Reuters ISI Web of Knowledge site.