  We present a detailed calculation of the transition temperature in QCD with
two light and one heavier (strange) quark mass on lattices with temporal extent
N_t =4 and 6. Calculations with improved staggered fermions have been performed
for various light to strange quark mass ratios in the range, 0.05 <= m_l/m_s <=
0.5, and with a strange quark mass fixed close to its physical value. From a
combined extrapolation to the chiral (m_l -> 0) and continuum (aT = 1/N_t -> 0)
limits we find for the transition temperature at the physical point T_c r_0 =
0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as
the distance in the static quark potential at which the slope takes on the
value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2. Using the currently best known value
for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV. The
transition temperature in the chiral limit is about 3% smaller. We discuss
current ambiguities in the determination of T_c in physical units and also
comment on the universal scaling behavior of thermodynamic quantities in the
chiral limit.
