Abstract: A radiation absorbing polymer having chemically bonded thereto a radiation absorbing dye, which has high absorption at a predetermined wavelength radiation, which shows good adhesion to a substrate and good thin film-forming, which has no dependence upon resists, which is soluble in a solvent for photoresists but becomes insoluble after being baked; a composition for radiation absorbing coating containing this polymer, and a radiation absorbing coating such as an anti-reflective coating formed from this composition are disclosed. The radiation absorbing polymer comprises a copolymer containing at least both a recurring unit composed of a monomer containing a keto group and a divalent group (preferably a methylene group) in its side chain and a recurring unit composed of a monomer containing an organic chromophore bonded directly or through a linkage group to the main chain. This radiation absorbing polymer is dissolved in a solvent such as alcohol, aromatic hydrocarbon, ketone, ester, etc.