  QCD at finite isospin chemical potential mu_I has no fermion sign problem and
can be studied on the lattice. We solve this theory analytically in two limits:
at low mu_I where chiral perturbation theory is applicable, and at
asymptotically high mu_I where perturbative QCD works. At low isospin density
the ground state is a pion condensate, whereas at high density it is a Fermi
liquid with Cooper pairing. The pairs carry the same quantum numbers as the
pion. This leads us to a conjecture that the transition from hadron to quark
matter is smooth, which passes several tests. Our results imply a nontrivial
phase diagram in the space of temperature and chemical potentials of isospin
and baryon number.
