  Using the linearly polarized intensity and polarization angle data at 3.6,
6.2 and 20 cm, we determine variations of Faraday rotation and depolarization
across the nearby galaxy M33. A 3-D model of the regular magnetic field is
fitted to the observed azimuthal distribution of polarization angles. Faraday
rotation, measured between 3.6 and 6.2 cm at a linear resolution of 0.7 kpc,
shows more variation in the south than in the north of the galaxy. About 10% of
the nonthermal emission from M33 at 3.6 cm is polarized. We estimate the
average total and regular magnetic field strengths in M33 as ~ 6.4 and 2.5
$\mu$G, respectively. Under the assumption that the disk of M33 is flat, the
regular magnetic field consists of horizontal and vertical components: however
the inferred vertical field may be partly due to a galactic warp. The
horizontal field is represented by an axisymmetric (m=0) mode from 1 to 3 kpc
radius and a superposition of axisymmetric and bisymmetric (m=0+1) modes from 3
to 5 kpc radius. An excess of differential Faraday rotation in the southern
half together with strong Faraday dispersion in the southern spiral arms seem
to be responsible for the north-south asymmetry in the observed wavelength
dependent depolarization. The presence of an axisymmetric m=0 mode of the
regular magnetic field in each ring suggests that a galactic dynamo is
operating in M33. The pitch angles of the spiral regular magnetic field are
generally smaller than the pitch angles of the optical spiral arms but are
twice as big as simple estimates based on the mean-field dynamo theory and
M33's rotation curve. Generation of interstellar magnetic fields from turbulent
gas motions in M33 is indicated by the equipartition of turbulent and magnetic
energy densities.
