Abstract: The NA60 experiment at the CERN SPS has measured muon pairs with unprecedented precision in 158 A GeV In-In collisions. A strong excess of pairs above the known sources is observed in the whole mass region 0.2 < M < 2.6 GeV. The mass spectrum for M < 1 GeV is consistent with a dominant contribution from pi (+) pi (-)->rho ->mu (+) mu (-) annihilation. The associated rho spectral function shows a strong broadening, but essentially no shift in mass. For M > 1 GeV, the excess is found to be prompt, not due to enhanced charm production, with pronounced differences to Drell-Yan pairs. The slope parameter T (eff) associated with the transverse momentum spectra rises with mass up to the rho, followed by a sudden decline above. The rise for M < 1 GeV is consistent with radial flow of a hadronic emission source. The seeming absence of significant flow for M > 1 GeV and its relation to parton-hadron duality is discussed in detail, suggesting a dominantly partonic emission source in ...