  Precision calculations of the fine and hyperfine structure of muonic atoms
are performed in a relativistic approach and results for muonic 205 Bi, 147 Sm,
and 89 Zr are presented. The hyperfine structure due to magnetic dipole and
electric quadrupole splitting is calculated in first order perturbation theory,
using extended nuclear charge and current distributions. The leading correction
from quantum electrodynamics, namely vacuum polarization in Uehling
approximation, is included as a potential directly in the Dirac equation. Also,
an effective screening potential due to the surrounding electrons is
calculated, and the leading relativistic recoil correction is estimated.
