  A new scheme based on (i) upcoming brilliant X-ray Free Electron Laser (FEL)
sources, (ii) novel energy and angular dispersive, large-area electron imagers
and (iii) the well-known photoelectron holography is elaborated that provides
time-dependent three-dimensional structure determination of small to medium
sized molecules with {\AA}ngstr\"om spatial and femtosecond time resolution.
Inducing molecular dynamics, wave-packet motion, dissociation, passage through
conical intersections or isomerization by a pump pulse this motion is
visualized by the X-ray FEL probe pulse launching keV photoelectrons within few
femtoseconds from specific and well-defined sites, deep core levels of
individual atoms, inside the molecule. On their way out the photoelectrons are
diffracted generating a hologram on the detector that encodes the molecular
structure at the instant of photoionization, thus providing 'femtosecond
snapshot images of the molecule from within'. Detailed calculations in various
approximations of increasing sophistication are presented and three-dimensional
retrieval of the spatial structure of the molecule with {\AA}ngstr\"om spatial
resolution is demonstrated. Due to the large photo-absorption cross sections
the method extends X-ray diffraction based, time-dependent structure
investigations envisioned at FELs to new classes of samples that are not
accessible by any other method. Among them are dilute samples in the gas phase
such as aligned, oriented or conformer selected molecules, ultra-cold ensembles
and/or molecular or cluster objects containing mainly light atoms that do not
scatter X-rays efficiently.
