This award is for continuing support of a program of fundamental investigations of physical phenomena important to understanding x-ray interactions with atoms and molecules. The primary scientific focus is probing the limits, especially at low photon energies, of the dipole approximation, the simplest reasonable treatment of photon interactions. Although well-known breakdowns of the dipole approximation exist (e.g., the dipole approximation is known to be completely invalid at photon energies greater than 20 keV), recent work of this program has demonstrated quantitatively significant breakdowns at surprisingly low energies and in unexpected ways; further studies may well lead to changes in some of the foundations of x-ray spectroscopy. The work proposed not only will further understanding of fundamental x-ray interactions, but determining the limits of the dipole approximation is important to myriad applications of x-ray absorption, x-ray photoemission, and x-ray fluorescence to other fields because these applications routinely assume the dipole approximation. In addition to the focus on nondipole effects in x-ray photoemission and x-ray fluorescence, related work is proposed on multi-atom resonance effects, transient species, and probing the limits of the independent-particle approximation.