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 (~42arcmin x 56arcmin) 3D-spectroscopic survey of the ionized gas disc of Messier 33. Fabry-Perot interferometry has been used to map its H{alpha} distribution and kinematics at unprecedented angular resolution (~<3 arcsec) and resolving power (~12600), with the 1.6 m 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 centre of the H{alpha} disc is distant from the photometric centre by ~168 pc (sky-projected distance) and that the kinematical major-axis position angle and disc inclination are in excellent agreement with photometric values. The H{alpha} rotation curve agrees very well with the HI rotation curves for 0<R<6.5 kpc, but the H{alpha} 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 H{alpha} velocity dispersion and the H{alpha} intensity. Mass models were obtained using the H{alpha} 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.