  We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis to
Teichmuller space. Let x be a point in Teichmuller space, and let B_R(x) be the
ball of radius R centered at x (with distances measured in the Teichmuller
metric).
  We obtain asymptotic formulas as R tends to infinity for the volume of
B_R(x), and also for for the cardinality of the intersection of B_R(x) with an
orbit of the mapping class group.
