  Studies of trapped quantum gases of bosons and of fermions have opened up a
new range of many-body problems, having a strong overlap with nuclear and
neutron star physics. Topics discussed here include: the Bose yrast problem --
how many-particle Bose systems carry extreme amounts of angular momentum; the
infrared divergent structure of the transition to Bose condensation in a weakly
interacting system; and the physics of extremely strongly interacting Bose and
Fermi systems, in the scale-free regime where the two body s-wave scattering
lengths are large compared with the interparticle spacing. Such a regime is
realized experimentally through use of atomic Feshbach resonances. Finally we
discuss creation of BCS-paired states in trapped Fermi gases.
