Luminous quasars at z>5.6 can be studied in detail with the current generation of telescopes and provide us with unique information on the first gigayear of the universe. Thus far, these studies have been statistically limited by the number of quasars known at these redshifts. Such quasars are rare, and therefore, wide-field surveys are required to identify them, and multiwavelength data are required to separate them efficiently from their main contaminants, the far more numerous cool dwarfs. In this paper, we update and extend the selection for the z~6 quasars presented in Banados+ (2014AJ....148...14B) using the Pan-STARRS1 (PS1) survey. We present the PS1 distant quasar sample, which currently consists of 124 quasars in the redshift range 5.6<~z<~6.7 that satisfy our selection criteria. Of these quasars, 77 have been discovered with PS1, and 63 of them are newly identified in this paper. We present the composite spectra of the PS1 distant quasar sample. This sample spans a factor of ~20 in luminosity and shows a variety of emission line properties. The number of quasars at z>5.6 presented in this work almost doubles the previously known quasars at these redshifts, marking a transition phase from studies of individual sources to statistical studies of the high-redshift quasar population, which was impossible with earlier, smaller samples.