Growing interest in the fields of core excited atomic, molecular and solid species has resulted in a demand for a compact, low cost laboratory source in the XUV (Extreme Ultra Violet) region of the spectrum. In contrast to the optical spectra of the valence electrons, which can mainly be described by the one-electron picture of the central field approximation, inner shell excitations are characterised by strong many electron effects causing the breakdown of the simple one-electron picture. Photoabsorption experiments provide valuable information on these many-electron correlation effects in atoms, excited atoms and ions. The measurement of photoionization cross sections of free ions pose considerable experimental difficulties, as a suitable absorbing column, of adequate density, must be produced and back lit by a bright, synchronised XUV continuum emitting source. Through the work reported in this thesis, a multi-laser, multi-channel spectrometer facility, for the measurement of photoionization cross sections of free atoms, excited atoms and ions, in the XUV has been developed. The facility is based on the DLP (Dual Laser Plasma) technique, whereby the absorbing column is produced by the ablation of spectroscopically pure targets, in vacuo, by either a flashlamp pumped dye laser (= 1 J in 2.5 p,s) or by a Q-switched ruby laser (~ 1.5 J in 30 ns). The synchronised XUV continuum source is generated by tightly focusing the output of a Nd:YAG laser (= 1 J in 15 ns) on a metal of high atomic number. Selection and isolation of the absorbing species of interest is achieved by an appropriate combination of laser type, target irradiation, spatial probing position of absorbing target and temporal separation of laser optical pulses.The continuum XUV radiation passes through the absorbing column and is collected by a toroidal mirror which efficiently couples the light into a 2.2 m grazing incidence spectrometer. The spectrometer is equipped with an MCP (Micro Channel Plate) self scanning diode array detector. The performance, capabilities and reliability of the facility have been demonstrated through the undertaking of a varied programme of XUV photoemission and photoabsorption experiments. The XUV photoabsorption characteristics of aluminium thin films, helium, argon,and free metal atoms and ions in the transition regions of the Periodic Table have been recorded. Where possible comparisons have been drawn against a background of recent significant experiments in the field.