Riemannian Nilmanifolds constitute the only known large family of Riemannian spaces on which non-trivial isospectral deformations take place profusely. All known
isospectral deformations within this family are constructed by means of continuous families of the so called almost inner automorphisms, a concept which originates
from the work of T. Sunada based on considerations of analogous problems in algebraic number theory. This work consists of an attempt at reviewing the related
ideas and culminates in a sketch of the important result of H. Pesce to the effect that isospectral deformations on step two Riemannian nilmanifolds can be obtained
only by means of continuous families of almost inner automorphisms.

Keywords : Riemannian manifold, Laplacian, spectrum, Lie groups, almost inner automorphisms, almost inner derivations, group representations, isospectral
deformation.