  Cosmological implications of clusters of galaxies are discussed with
particular attention to their importance in probing the cosmological
parameters. More specifically we compute the number counts of clusters of
galaxies, Log $N$ -- Log $S$ relation, in X-ray and submm bands on the basis of
the Press--Schechter theory. As an important step toward breaking the
degeneracy among the viable cosmological models, we observed the most luminous
X-ray cluster RXJ1347-1145 in three bands (21 and 43 GHz in the Nobeyama Radio
Observatory, Japan, and 350 GHz in the J. C. Maxwell telescope at Mauna Kea,
Hawaii). We report on the preliminary results which are in good agreement with
the profile of the Sunayev -- Zel'dovich effect predicted on the basis of the
previous X-ray observation of the cluster.
