We plan  to cover in five talks  the following topics:

1. The Classical Model

We will discuss the classical setup of Moebius geometry as
a subgeometry of projective geometry. Also we shall see
how the space form geometries arise as subgeometries
of Moebius geometry.

2. Curved Flats

Curved flats are a certain type of integrable system in
symmetric (or reductive homogeneous) spaces.
We shall discuss curved flats in the space of point pairs
in the 3-sphere and, possibly, in the space of circles in
the conformal 4-sphere.

3. A Quaternionic Formalism

Moebius transformations of the conformal 3- and 4-spheres can
be descibed as quaternionic linear fractional transformations.
This approach provides a nice and efficient way to study the
geometry of surfaces in the 3-sphere.
We shall see how this approach links up with the classical
approach.

4. Isothermic Surfaces

We will study the transformation theory of isothermic surfaces
using the developed quaternionic formalism. I hope to make a
link with the curved flats approach and to explain the various
Bianchi permutability theorems.

5. Conclusions

This lecture will be open for requests: topics that could be
addressed range from Willmore surfaces, recent developments
on conformally flat hypersurfaces, more in-depth study of
isothermic surfaces and cmc surfaces to discrete isothermic
nets and their transformations.