We have updated the isotopically invariant Dunham fit of O2 with newly reported literature transitions to derive (1) the energy levels, partition sums, band-by-band molecular constants, and RKR potentials for the X3 Sigma−g , a1 Delta g, and b1 Sigma+g states of the six O2 isotopologues: 16O16O, 16O17O, 16O18O,17O17O, 17O18O, and 18O18O; (2) Franck-Condon factors for their a1 Delta g − X3 Sigma−g , b1 Sigma+g − X3 Sigma−g , and a1 Delta g − b1 Sigma+g band systems. This new spectroscopic parameterization characterizes all known transitions within and between the X3 Sigma−g , a1 Delta g, and b1 Sigma+g states within experimental uncertainty and can be used for accurate predictions of as yet unmeasured transitions. All of these results are necessary to provide a consistent linelist of all transitions which will be reported in a followup paper.