Muller's academic study of Buddhism began as an undergraduate at Stony Brook University, where he majored in Religious Studies under the guidance of Sung Bae Park, a specialist in Seon and Korean Buddhism. After graduating, he spent two years studying in Japan, after which he spent one year in the graduate program in Religious Studies at the University of Virginia. In 1988, he left UVa to return to Stony Brook, where he completed a PhD in Comparative literature, once again with Sung Bae Park as his principal advisor. He also studied Christian Theology with Peter Manchester, Islam with William Chittick, and Postmodern literary criticism with Michael Sprinker and Hugh Silverman. His dissertation, "Hamhŏ Kihwa: A Study of His Major Works," was accepted in 1993, after which he spent six months in Korea as a research associate at the Academy of Korean Studies, before taking up an academic position in Japan, at Toyo Gakuen University.
From 1994 to 2008, Muller taught courses in philosophy and religion at Toyo Gakuen University, during which time he published numerous books and articles on Korean Buddhism, Zen, East Asian Yogacara, and Confucianism. While active in numerous academic organizations such as the American Academy of Religion and the Japanese Association for Indian and Buddhist Studies, he also became known as one of leading figures in the creation of online research resources. In 1995, he set up his web site called Resources for East Asian Language and Thought (still in active service today), featuring online lexicons, indexes, bibliographies, and translations of classical texts. In 1996, he started the Budschol listserv for the academic study of Buddhism, which would, in 2000, become part of H-Net, under the name of H-Buddhism, the central internet organ for communication among scholars of Buddhism. He also initiated two major dictionary projects, the Digital Dictionary of Buddhism and the CJKV-E Dictionary, which have become basic reference works for the field of Buddhist and East Asian studies, subscribed to by universities around the world. His work in the area of online reference works and digitization led him into the field of Digital Humanities, with his principal area of expertise lying in the handling of literary documents using XML and XSLT. In 2008, Muller was invited to join the Faculty of Humanities at the University of Tokyo, where he taught courses in Digital Humanities, Chinese Philosophy, and Korean Philosophy and Religion. He retired from UTokyo in March 2019 and moved to Musashino University, where he is director of the Institute of Buddhist culture and teaches courses in Buddhist Studies. (Source Accessed July 21, 2021)