We report the discovery of 34 stars in the Hamburg/ESO Survey for metal-poor stars and the Sloan Digital Sky Survey that have [ Fe/H ] \lesssim –3.0 . Their median and minimum abundances are [ Fe/H ] = –3.1 and –4.1 , respectively , while 10 stars have [ Fe/H ] < –3.5 . High-resolution , high- S / N spectroscopic data – equivalent widths and radial velocities – are presented for these stars , together with an additional four objects previously reported or currently being investigated elsewhere . We have determined the atmospheric parameters , effective temperature ( T _ { eff } ) and surface gravity ( \log g ) , which are critical in the determination of the chemical abundances and the evolutionary status of these stars . Three techniques were used to derive these parameters . Spectrophotometric fits to model atmosphere fluxes were used to derive T _ { eff } , \log g , and an estimate of E ( B - V ) ; H \alpha , H \beta , and H \gamma profile fitting to model atmosphere results provided the second determination of T _ { eff } and \log g ; and finally , we used an empirical T _ { eff } -calibrated H \delta index , for the third , independent T _ { eff } determination . The three values of T _ { eff } are in good agreement , although the profile fitting may yield systematically cooler T _ { eff } values , by \sim 100 K. This collective data set will be analyzed in future papers in the present series to utilize the most metal-poor stars as probes of conditions in the early Universe .