High Harmonic Generation is a highly nonlinear process that can be used to generate a high flux, low divergence, coherent beam in the extreme ultraviolet (XUV) wavelength range. It is proposed that this radiation source could be implemented for microscopy using coherent diffractive imaging, with potential measurements including the shape characterisation of single proteins and other biological samples. This thesis documents the development of the diffraction beam line at the University of Southampton, and presents experimental results that show progress towards this goal. A spherical multilayer mirror and a tapered hollow fiber have been used to focus the XUV beam. The mirror produced an astigmatic focus as a result of the off-axis geometry. Analysis of the surface quality of the mirror enabled an explanation for the observed interference peak splitting. The fiber was found to produce a smaller focus, but suffered from a degraded beam quality due to multiple reflections inside the optic. Using a phase retrieval algorithm, an experimental XUV diffraction pattern has been used to determine the shape of a micron-sized sample. Fresnel diffraction from an array of micron-sized apertures has been simulated and experimentally verified. A technique for simultaneously measuring the structure and dielectric constant of a nanosized periodic sample, for multiple wavelengths, is presented. This is achieved by using the Mie solution to model the diffraction peak intensities from a hexagonal array of 196 nm diameter polystyrene spheres. Refractive index results are given for the range 25 to 30 nm and are found to disagree with tabulated values.