Improved method for the production of a polymer of a monofunctional (unsaturated) monomer, particularly polymethyl methacrylate, by a rapid crosslinking polymerization, which comprises polymerizing a mixture of a monofunctional (unsaturated) monomers, selected from methyl methacrylate and a monomer mixture comprising predominantly methyl methacrylate which may partially contain a polymer of the monomer (i.e. a syrup of the monomer or monomer mixture), and a polyfunctional (unsaturated) monomer in the presence of (1) a radical polymerization initiator, (2) a reducing compound containing sulfur in the molecule thereof, (3) an amine hydrohalogenate or a quaternary ammonium halide and (4) a copper-containing compound. Said polymer has high mechanical properties and excellent transparency and is useful particularly for the production of optical parts such as conventional lenses, Fresnel's lens, optical recording disc media, prisms, mirrors, etc.