We investigate the process of galaxy formation as can be observed in the only currently forming galaxies -- the so-called Tidal Dwarf Galaxies, hereafter TDGs -- through observations of the molecular gas detected via its CO (Carbon Monoxide) emission. Molecular gas is a key element in the galaxy formation process, providing the link between a cloud of gas and a {\\it bona fide} galaxy. We have now detected CO in 9 TDGs with an overall detection rate of 80%, showing that molecular gas is abundant in TDGs, up to a few $10^8 M_\\odot$. The CO emission coincides both spatially and kinematically with the HI emission, indicating that the molecular gas forms from the atomic hydrogen where the HI column density is high. A possible trend of more evolved TDGs having greater molecular gas masses is observed, in accord with the transformation of HI into H$_2$. Although uncertainties are still large for individual objects as the geometry is unknown, we find that the \"dynamical\" masses of TDGs, estimated from the CO line widths, do not seem to be greater than the \"visible\" masses (HI + H$_2$ + a stellar component), i.e., TDGs require no dark matter. We provide evidence that TDGs are self-gravitating entities, implying that we are witnessing the ensemble of processes in galaxy formation: concentration of large amounts of gas in a bound object, condensation of the gas, which is atomic at this point, to form molecular gas and the subsequent star formation from the dense molecular component.