Isospectral, non-isometric Riemannian manifolds

summary:The author gives a survey of the history of isospectral manifolds that are non-isometric discussing the work of Milnor, Vign\'eras, Sunada, and de Turck and Gordon. She describes the construction of continuous isospectral deformations as introduced by Gordon, Wilson, De Turck et al. She also discusses the construction of isospectral plane domains due to Gordon, Webb, and Wolpert. Some new examples of isospectral non-isometric manifolds are given