High-resolution long-slit spectra in the 6250-6800 angstrom range, obtained at various position angles from the emission nebulosities around T Tau, are presented. Using a method recently developed by Solf, we have eliminated the contribution of the stellar continuum spectrum to the detected emission lines and determined position-velocity diagrams of the [O I], [N II], and [S II] lines in the immediate vicinity of the star. We identify at least five individual components (A, B, C, D, and E) in the complex emission-line structure which are distinguished by their spatial distribution and their related kinematic properties. Each line component can be attributed to a separate nebular condensation in the mass outflows associated with the T Tau system. Two line components (A and B) are analogues to those observed in other T Tauri stars and seem to be due to a slow disk wind (A) and a fast stellar wind (B). Component A presents a centroid velocity of approximately -9 km s-1 with respect to the stellar velocity and is offset toward NW from the optical stellar component T Tau N by approximately 1.1'' and approximately 0.1'' in [S II] and [O I], respectively. Component B presents a centroid velocity of approximately -120 km s-1 and maximum velocities up to approximately -175 km s-1 at approximately 3'' W of the star. Most likely, component B represents the approaching part of a bipolar jet emanating from T Tau N and pointing toward W, whose receding counterpart is obscured by a circumstellar disk. The jet is already highly collimated at only approximately 0.3'' (approximately 50 AU) from the star and ultimately leads to the formation of the Herbig-Haro object in NGC 1555. The other three line components have no analogues in other T Tauri star systems. Two of them (C and D) from a second bipolar outflow system of moderate collimation. The orientation of its flow axis is near the N-S direction and hence significantly different from that of the jet seen in component B. The centroids of the northern lobe (C) and southern lobe (D) are separated from T Tau N by 0.9'' and 1.3'', respectively; the magnitudes of their centroid velocities with respect to the stellar velocity are approximately the same (approximately 43 km s-1). In both lobes, the radial velocity drops to about zero at a distance of approximately 4'' from the star. Arguments are presented suggesting that the starlike infrared source T Tau S may be the origin of the bipolar outflow C-D. Component E represents an extended structure with a Herbig-Haro spectrum and has been attributed to ''Burnham's nebula'' S of T Tau. In component E, the derived mean relative radial velocity of approximately -5 km s-1 and the velocity dispersion of approximately 25 km s-1 (FWHM) seem to indicate a rather low shock velocity, although the observed line ratios suggest shock-excited gas with a shock velocity of typically 90 km s-1. In this sense, the structure of Burnham's nebula is enigmatic. Our data seem to indicate that there exists a kinematical and physical connection between the southern lobe (D) of the bipolar outflow C-D and component E. This would imply that a significant deceleration of the outflowing gas occurs in the region where Burnham's nebula is formed.
