Galaxy clusters, the largest well-defined structures in the universe, were found to be the most luminous class of X-ray sources in the universe. The X-ray emission originates from the intracluster medium (ICM), a hot (10^7-10^8 K), low density (10^{-4}-10^{-2} protons cm^{-3}), and diffuse plasma in the inter-galaxy space. The X-ray continuum from the ICM is primarily produced via free-free emission process, working between electrons and ions in the ICM. In addition, collisions of electrons with ions of abundant elements in the ICM produce the emission lines.

As an example of recent X-ray spectroscopic study of clusters, I will present measurements of the elemental abundances in the ICM. Along with detailed Si, S and Fe radial abundance distributions the O abundances are accurately derived. The Fe abundance maxima towards the cluster center, possibly due to the metals from the central galaxy, are spatially resolved. The Si and S abundances also exhibit central increases in general, resulting in uniform Fe-Si-S ratios within the cluster. In contrast, the O abundances are in general uniform over the cluster. The obtained results are used to discuss the past star formation history in clusters.

In addition, I will introduce some prospects of future X-ray study by a Japanese-US X-ray astronomy satellite Astro-E2, which will be launched on early 2005. An X-ray micro-calorimeter (XRS) on the observatory will provide X-ray spectral　capability better than any previous instruments, with the energy resolution of　about 6 eV in the 0.3-10 keV energy band. This instrument should provide detailed and precise measurements of the elemental abundance in the ICM.