  Quantum chromodynamics (QCD) at finite temperature (T), baryon chemical
potential (\muB) and isospin chemical potential (\muI) is studied in the strong
coupling limit on a lattice with staggered fermions. With the use of large
dimensional expansion and the mean field approximation, we derive an effective
action written in terms of the chiral condensate and pion condensate as a
function of T, \muB and \muI. The phase structure in the space of T and \muB is
elucidated, and simple analytical formulas for the critical line of the chiral
phase transition and the tricritical point are derived. The effects of a finite
quark mass (m) and finite \muI on the phase diagram are discussed. We also
investigate the phase structure in the space of T, \muI and m, and clarify the
correspondence between color SU(3) QCD with finite isospin density and color
SU(2) QCD with finite baryon density. Comparisons of our results with those
from recent Monte Carlo lattice simulations on finite density QCD are given.
