A multi-functional admixture for simultaneously providing specified characteristics to hydraulic cement compositions such as concrete contains one or more of specified reaction mixtures obtained by specified two processes as well as partially or completely neutralized substances obtained from such a reaction mixture through a specified third process. The specified two processes include initiating a radical copolymerization process of a radical polymerizable monomer mixture containing maleic anhydride and a monomer of a specified kind in a non-aqueous system in the presence of a non-aqueous radical initiator and stopping the radical copolymerization reaction in its midst while the inversion rate of polymerization is at a specified level by adding water to the reaction system to thereby obtain a reaction mixture. The specified third process is for partially or completely neutralizing the reaction mixture.