Audrey Terras is a fellow of the American Association for the Advancement of Science and has served on that organization's mathematics section nominating committee. She has served on the Council of the American Mathematical Society and various AMS committees and was an editor of the Transactions of the AMS. Currently she is an associate editor of book reviews for the Bulletin of the AMS and the chair of the Western Section Program Committee. She has served on various AWM committees in the past.
She has written three books: Harmonic Analysis on Symmetric Spaces and Applications, Vols. I, II, Springer-Verlag, New York, 1985, 1988 and Fourier Analysis on Finite Groups and Applications, Cambridge University Press, Cambridge, 1999. She also co-edited, with Dennis Hejhal and Peter Sarnak, the proceedings from a 1984 conference on Selberg's trace formula. Her research interests include number theory; harmonic analysis on symmetric spaces and finite groups along with its applications; special functions; algebraic graph theory, especially zeta functions of graphs; and Selberg's trace formula.
Current research involves finite analogues of the symmetric spaces of her Springer-Verlag volumes. This led her to work on spectra of graphs and hypergraphs attached to finite matrix groups, also coverings of graphs and their zeta and L-functions. These functions are analogues of the Riemann and Selberg zeta functions.