There are several reasons why clusters of galaxies are regarded as useful tools in cosmology; (i) since the dynamical time-scale of clusters is comparable to the age of the universe, they should retain the cosmological initial conditions fairly faithfully, (ii) clusters can be observed in various wavelengths including optical, X-ray, radio, mm and submm bands, and recent and future big projects (e.g., SDSS, AXAF, PLANCK) aim to make extensive surveys and detailed imaging/spectroscopic observations of clusters, (iii) to the first order approximation, clusters can be regarded as a simple system of dark matter, gas and galaxies, and thus theoretically well-defined and relatively well-understood, at least compared with galaxies themselves, (iv) clusters of galaxies can be observed up to high redshifts and thus provide a probe of the distant universe.
X-ray observations are particularly suited for the study of clusters,
because the X-ray emissivity is proportional to 
and less
sensitive to the projection contamination which has been known to be a
serious problem in their identifications with the optical data. In
addition, the Sunyaev -- Zel'dovich (SZ) effect (Sunyaev & Zel'dovich
1972), observed in radio, millimeter and submillimeter bands, is now
opening a new window to investigating cluster properties, especially
at high redshifts. In this paper, we aim to show the significance of
current and future observations in these bands in cosmology.