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Aims. As the nearest large spiral galaxy, M31 provides a unique opportunity to study the structure and evolutionary history of this galaxy type in great detail. Among the many observing programs aimed at M31 are microlensing studies, which require good threedimensional models of the stellar mass distribution. Possible non-axisymmetric structures like a bar need to be taken into account. Due to M31's high inclination, the bar is difficult to detect in photometry alone. Therefore, detailed kinematic measurements are needed to constrain the possible existence and position of a bar in M31. Methods. We obtained ≈220 separate fields with the optical integral-field unit spectrograph VIRUS-W, covering the whole bulge region of M31 and parts of the disk. We derived stellar line-of-sight velocity distributions from the stellar absorption lines, as well as velocity distributions and line fluxes of the emission lines Hβ, [O III] and [N I]. Our data supersede any previous study in terms of spatial coverage and spectral resolution. Results. We find several features that are indicative of a bar in the kinematics of the stars, we see intermediate plateaus in the velocity and the velocity dispersion and correlation between the higher moment h3 and the velocity. The gas kinematics is highly irregular, but is consistent with non-triaxial streaming motions caused by a bar. The morphology of the gas shows a spiral pattern, with seemingly lower inclination than the stellar disk. We also look at the ionization mechanisms of the gas, which happens mostly through shocks and not through starbursts. [ABSTRACT FROM AUTHOR]