  We construct several new classes of isospectral manifolds with different
local geometries. After reviewing a theorem by Carolyn Gordon on isospectral
torus bundles and presenting certain useful specialized versions (Chapter 1) we
apply these tools to construct the first examples of isospectral
four-dimensional manifolds which are not locally isometric (Chapter 2).
Moreover, we construct the first examples of isospectral left invariant metrics
on compact Lie groups (Chapter 3). Thereby we also obtain the first continuous
isospectral families of globally homogeneous manifolds and the first examples
of isospectral manifolds which are simply connected and irreducible. Finally,
we construct the first pairs of isospectral manifolds which are conformally
equivalent and not locally isometric (Chapter 4).
