The structure of the resonance line ⋋553.5 nm of Ba ɪ has been studied by means of Doppler-free spectroscopy. Dye laser light was scattered resonantly from an atomic beam containing the natural mixture of isotopes; the spectra were recorded digitally and analysed by computer. The main object was to provide data to reduce uncertainties due to electronic calculations in the extraction of nuclear data from optical measurements. The isotope shifts (MHz), relative to 138 Ba, are 137 Ba, – 214.7 (5); 136 Ba, – 127.5 (13); 135 Ba, – 258.7 (7); 134 Ba, – 142.8 (12). The minus signs indicate that 138 Ba has the lower frequency in each case. These results are combined with muonic X-ray, electronic X-ray and other optical data to extract changes in mean square radius of the nuclear charge distribution. The hyperfine splitting factors 135 A and 135 B were found to be – 97.76 (14) MHz and 32.29 (47) MHz respectively. From an analysis of these and other results for the 6s6p configuration we obtain the quadrupole moment of 135 Ba (uncorrected for quadrupole shielding) to be 0.195 (40) barn (1 barn = 10 -28 m 2 ).