  We put forward a first-principle NonEquilibrium Green's Function (NEGF)
approach to calculate the transient photoabsorption spectrum of optically thin
samples. The method can deal with pump fields of arbitrary strength, frequency
and duration as well as for overlapping and nonoverlapping pump and probe
pulses. The electron-electron repulsion is accounted for by the correlation
self-energy, and the resulting numerical scheme deals with matrices that scale
quadratically with the system size. Two recent experiments, the first on helium
and the second on krypton, are addressed. For the first experiment we explain
the bending of the Autler-Townes absorption peaks with increasing the
pump-probe delay $\t$, and relate the bending to the thickness and density of
the gas. For the second experiment we find that sizable spectral structures of
the pump-generated admixture of Kr ions are fingerprints of {\em dynamical
correlation} effects, and hence they cannot be reproduced by time-local
self-energy approximations. Remarkably, the NEGF approach also captures the
retardation of the absorption onset of Kr$^{2+}$ with respect to Kr$^{1+}$ as a
function of $\t$.
