  An overview of the authors results is given. Property C for ODE is defioned,
It is proved that the pair of Sturm-Liouville operators has property C. This
property is applied to many inverse problems. Some well-known results, such as
uniqueness of the recovery of the potential from scattering data, from the
spectral function and from two spectra are proved in a new short way based on
property C. Many new results are obtained. In particular, it is proved that a
compactly supported potential can be uniquely recovered from the phase shift of
s-wave alone, known at all energies, without knowledge of bound states and
norming constants. The fixed-energy phase shifts known at some values of the
angular momentum determine a compactly supported potential uniquely. Mixed data
inverse problems are studied. Analysis of the Newton-Sabatier procedure is
given. It is shown that this procedure is a parameter-fitting procedure rather
than an inversion method. Other results on inverse problems are obtained.
