Excitation and fluorescence spectra of the Cs2 molecule were measured with high resolution allowing resolution of the rotational structure. These spectra were studied under excitation by different lines of a single mode argon laser which could be continuously tuned across spectral intervals of about 10 GHz. For excitation in a cesium vapor cell the spectral resolution was only limited by the Doppler width of the absorption lines while in a collimated cesium beam a resolution between 20 and 60 MHz could be achieved. Accurate molecular constants and the RKR potential of the X 1Σ+g ground state are derived from more than 900 fluorescence lines, most of which were precisely measured with a Fabry–Perot interferometer crossed with a monochromator. The dissociation energy of the ground state is deduced from an extrapolation beyond the highest measured level with v″=72, and also from a second laser-excited fluorescence spectrum that appears at the red end of the singlet spectrum and consists of a continuum and a few discrete lines. This spectrum is assigned to transitions terminating in the X 3Σ+u state, which is mainly repulsive. Like the X 1Σ+g state, it too dissociates into two Cs atoms in their 6 2S1/2 ground states.