Son of two teachers, Alan Brissenden was educated at Cowra High School, Sydney University (BA Hons, Dip.Ed.) and London University (PhD). He was a teacher and then a research officer for the NSW Department of Education in the 1950s. He also taught at Adelaide University 1963-1994 (Senior Lecturer 1968-1982, Reader 1982-1994), later continuing there as an Honorary Visiting Research Fellow. He was also a Visiting Fellow at the Huntingdon Library, Pasadena, and Wolfson College, Oxford.
Brissenden grew up in country where some of the incidents fictionalised in Boldrewood's Robbery Under Arms took place. He edited and introduced a facsimile edition of Boldrewood's novel, and edited some works by Henry Lawson. He also wrote and edited several books on William Shakespeare.
Brissenden was well known as a reviewer and as a dance critic. He was involved in a number of Australian and international organisations concerned with literature and the arts, including the Adelaide Festival of Arts, the Adelaide branch of the English Association, the Arts Council of South Australia, the Australian and New Zealand Shakespeare Association, Friends of the State Library of South Australia and the Australian Dance Council. He chaired the Early Imprints Project in South Australia from 1977, and he edited Early Printed Books in South Australia: The Catalogue of the Early Imprints Project in South Australia (electronic resource, 1994).
Brissenden was awarded an AM in 1996 for service to the arts as a promoter and critic of drama and dance, and as a member of the Board of Governors of the Adelaide Festival.
Brother of R. F. Brissenden (qv).