The properties of the Kamiokande-II detector and the method of measurement are described in detail. The data on the neutrino burst from the supernova SN1987A on 23 February 1987 at 7:35:35 UT\ifmmode\pm\else\textpm\fi{}1 min are presented, with records of earlier and later observation periods in which other neutrino events possibly associated with SN1987A might have occurred. There is no evidence in the data for any excess of neutrino-induced events, either in a burst of a few seconds duration or over a longer time interval, relative to the usual count rate, excepting only the neutrino burst at 7:35:35 UT. The nature of the single, observed neutrino burst coincides remarkably well with the elements of the current model of type-II supernovae and neutron-star formation. This is the first direct observation in neutrino astronomy.