  Isoscalar giant resonances are nuclear collective excitations associated with
the oscillation in phase of protons and neutrons according to a certain
multipolarity $L$. In particular, the isoscalar giant monopole resonance
($L=0$) is the strongest nuclear compression mode, and its excitation energy is
directly related to the compression modulus for finite nuclei. Typically,
microscopic calculations are utilized to establish a relationship between the
experimental compression modulus and the nuclear incompressibility that is a
crucial parameter of the equation of state for nuclear matter. The
incompressibility of nuclear matter has been determined with an accuracy of 10
to 20\% using relativistic and non-relativistic microscopic models for
describing the monopole distributions in ${}^{208}$Pb and ${}^{90}$Zr isotopes.
However, the same theoretical models are not able to describe data for
open-shell nuclei, such as those of tin and cadmium isotopes. In fact, only
effective interactions with a softer nuclear-matter incompressibility are able
to predict the centroid energy of monopole distributions for open-shell nuclei.
An unified description of the monopole resonance in ${}^{208}$Pb and other
open-shell nuclei remains unsolved from the theory side. Most of this
uncertainty is due to our poor knowledge of the symmetry energy, which is
another essential component of the equation of state of nuclear matter.
Therefore, new experimental data along isotopic chains covering a wide range in
$N/Z$ ratios, including neutron-deficient and neutron-rich nuclei, are of
paramount importance for determining both the nuclear-matter incompressibility
and the symmetry energy more precisely.
