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Using Gaia DR2 astrometry, we map the kinematic signature of the Galactic stellar warp out to a distance of 7 kpc from the Sun. Combining Gaia DR2 and 2MASS photometry, we identify, via a probabilistic approach, 599 494 upper main sequence stars and 12 616 068 giants without the need for individual extinction estimates. The spatial distribution of the upper main sequence stars clearly shows segments of the nearest spiral arms. The large-scale kinematics of both the upper main sequence and giant populations show a clear signature of the warp of the Milky Way, apparent as a gradient of 5-6 km/s in the vertical velocities from 8 to 14 kpc in Galactic radius. The presence of the signal in both samples, which have different typical ages, suggests that the warp is a gravitationally induced phenomenon.