We present an extensive dataset of highly accurate absolute travel times and travel-time residuals of tele-seismic P waves recorded by the AlpArray Seismic Network and complementary field experiments in the years from 2015 to 2019. The dataset is intended to serve as the basis for teleseismic travel-time tomography of the upper mantle below the greater Alpine region. In addition, the data may be used as constraints in full-waveform inversion of AlpArray recordings. The dataset comprises about 170 000 onsets derived from records filtered to an upper-corner frequency of 0.5 Hz and 214 000 onsets from records filtered to an upper-corner frequency of 0.1 Hz. The high accuracy of absolute and residual travel times was obtained by applying a specially designed combination of automatic picking, waveform cross-correlation and beamforming. Taking travel-time data for individual events, we are able to visualise in detail the wave fronts of teleseismic P waves as they propagate across AlpArray. Variations of distances between isochrons indicate structural perturbations in the mantle below. Travel-time residuals for individual events exhibit spatially coherent patterns that prove to be stable if events of similar epicentral distance and azimuth are considered. When residuals for all available events are stacked, conspicuous areas of negative residuals emerge that indicate the lateral location of subducting slabs beneath the Apennines and the western, central and eastern Alps. Stacking residuals for events from 90 degrees wide azimuthal sectors results in lateral distributions of negative and positive residuals that are generally consistent but differ in detail due to the differing direction of illumination of mantle structures by the incident P waves. Uncertainties of travel-time residuals are estimated from the peak width of the cross-correlation function and its maximum value. The me-dian uncertainty is 0.15 s at 0.5 Hz and 0.18 s at 0.1 Hz, which is more than 10 times lower than the typical travel-time residuals of up to +/- 2 s. Uncertainties display a regional dependence caused by quality differences between temporary and permanent stations as well as site-specific noise conditions.