As part of a long-term project to revisit the kinematics and dynamics of the large disc galaxies of the Local Group, we present the first deep, wide-field (42' x 56') 3D-spectroscopic survey of the ionized gas disc of Messier 33. Fabry-Perot interferometry has been used to map its Ha distribution and kinematics at unprecedented angular resolution (<3'') and resolving power (12600), with the 1.6m telescope at the Observatoire du Mont Megantic. The ionized gas distribution follows a complex, large-scale spiral structure, unsurprisingly coincident with the already-known spiral structures of the neutral and molecular gas discs. The kinematical analysis of the velocity field shows that the rotation center of the Ha disc is distant from the photometric center by 170 pc (sky projected distance) and that the kinematical major-axis position angle and disc inclination are in excellent agreement with photometric values. The Ha rotation curve agrees very well with the HI rotation curves for 0 < R < 6.5 kpc, but the Ha velocities are 10-20 km/s higher for R > 6.5 kpc. The reason for this discrepancy is not well understood. The velocity dispersion profile is relatively flat around 16 km/s, which is at the low end of velocity dispersions of nearby star-forming galactic discs. A strong relation is also found between the Ha velocity dispersion and the Ha intensity. Mass models were obtained using the Ha rotation curve but, as expected, the dark matter halo's parameters are not very well constrained since the optical rotation curve only extends out to 8 kpc.Read less <