Inner shell ionization and excitation in atoms has been studied extensively for many decades using a variety of ultraviolet and X-ray light sources, especially, but not exclusively, synchrotrons. In addition, the study of multiphoton absorption by outer (valence) electrons rapidly followed the development of sufficiently intense optical and infrared laser systems. The advent of intense EUV and X-ray Free Electron Lasers (FELs), based on the principle of Self Amplifed Spontaneous Emission (SASE), has enabled the study of multiphoton ionization of inner shell electrons for the first time. Results on the interaction of intense and ultrashort extreme ultraviolet FEL pulses with a specific focus on multiphoton ionization of neon, krypton and xenon are presented in this thesis. As a guide, some common FEL parameters utilised as part of experiments presented here included pulse energies of up to 50 μJ with average (envelope) durations of 30 fs for photon energies of 46 eV and 93 eV, with a beam diameter of typically 3 mm (unfocused) and focussed spot sizes of < 50 microns. A tightly focused FEL beam at 93 eV hence results in intensities on the order of 10^16 W.cm^−2 In a complementary experiment, ionization of a singly ionised Ne target by combining EUV radiation from FLASH with an intense, synchronized optical laser was investigated. The ejected electrons undergo stimulated emission and absorption in the presence of the IR field, creating so-called ’sidebands’ in the photoelectron spectrum. It was found that the photoelectron spectra exhibit a strong dependence on the relative polarisation of the two fields as well as the magnetic substates of the residual doubly-charged ionic core. This experiment utilised a second, IR laser, the pulses of which were spatially and temporally overlapped with those of the FEL. For reference, the 800 nm IR laser was operated in both ’long’ (3 ps) and ’short’ (120 fs) pulse modes, with ’long’ mode used for coarse synchronisation purposes. Typically, the IR laser was focused to a spot size on the order of 50 microns.