I present an investigation into the X-ray properties of galaxy clusters, consisting of a principal component analysis of ROSAT data and studies of three clusters observed with the XMM-Newton satellite. The principal component analysis provides an investigation into similarities between cluster surface brightness profiles. Initial results for 42 clusters are presented and compared to existing models. The cluster profiles are reproduced to good accuracy using three principal components. Correlation of the principal components to physical properties is investigated but the results are inconclusive. Observations of Abell 1413, Abell 665 and Abell 2163 made with XMM-Newton were investigated spectrally and spatially to determine cluster properties. Global temperatures were found to be 7.08 +/- 0.140.13 keV for Abell 665 and 11.98 +/- 1.2 keV for Abell 2163. The temperature and abundance profiles of the clusters are very different, with some differences attributed to the recent merging of subclusters in Abell 665 and Abell 2163. Spatial analysis of the cluster surface brightness profiles is undertaken with beta and NFW models. The profiles produced for the three clusters are used to estimate the variation of gas, gravitational and iron mass with radius. These are used to draw general conclusions, such supernovae numbers (NSNII 109--11). The cosmological density and matter density parameters are found; &OHgr;0 = 0.22 -- 0.33 +/- 0.1 and &OHgr; m ? 0.12+/-0.060.04. This suggests a low density universe, but is subject to uncertainty due to extrapolation to larger radii.