Twisted Isospectrality, Homological Wideness, and Isometry: A Sample of Algebraic Methods in Isospectrality

The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings).
The methods outlined in the book fit into the tradition of the famous work of Sunada...