Physical properties in infrared dark clouds (IRDCs) provide insights into how high-mass stars and stellar clusters form. We have conducted the ALMA Survey of 70 µm Dark High-mass Clumps in Early Stages (ASHES) toward thirty-nine clumps that are dark at 24 µm and 70 µm, cold, massive, and dense, the best sample to study the earliest stage of the high-mass star formation. The high-resolution (~1.”2) and high-sensitivity observations mosaicked by ALMA succeed in revealing the internal structure of IRDCs and an unprecedented number of 839 cores. We find less than 1% of cores have masses higher than 27 Msun, and these are all gravitationally bound and associated with molecular outflows. There is no high-mass (>27 Msun) prestellar core; all most massive cores have outflows and line emission consistent with warm gas. Additionally, 90% of our sample (35/39) only host low- to intermediate-mass cores, implying the necessity of additional mass feeding to form high-mass stars. We also find a weak correlation between the maximum core mass in each clump and their clump mass contrary to the strong correlation found in stellar clusters between the maximum stellar mass and cluster mass, implying that the maximum core mass is not determined by the natal clump mass at least in the very early stages traced in ASHES. Although we identified hub-filament systems in half of our sample, we find no preferred locations for the formation of the most massive cores and only a few tentative detections of mass segregation. Our findings imply that hub-filament systems are not yet efficiently contributing to core accretion at the earliest stages of high-mass star and cluster formation.