  Effective field theory of the in-medium nucleon-nucleon interaction is
considered. The effective range parameters are found to be of a natural scale.
The low density limit is discussed both in perturbative and nonperturbative
situations. In the nonperturbative case the attractive character of the
nucleon-nucleon interactions in the $^{1}S_0$ channel leads to the nuclear
superfluidity which is analyzed in the framework of the renormalization group.
The numerical values of the corresponding energy gap are in agreement with
results obtained by more more traditional many-body techniques. The S-wave part
of potential energy per particle is calculated for different values of nuclear
density. The role of pion and many-body effects is discussed. Problems and
challenges in constructing the chiral theory of nuclear matter are outlined.
