Azurite (Cu-3(CO3)(2)(OH)(2)) is a model substance of a diamond spin chain, one of frustrated antiferromagnetic quantum spin chains. The high field magnetization up to 60 T, magnetic susceptibility, magnetic entropy, muon spin relaxation and H-1-NMR of azurite have been measured using single crystals. A distinct 1/3 magnetization plateau is confirmed to be present in the magnetization curve. Two resonance peaks of H-1-NMR were observed. By analyzing temperature dependencies of their hyperfine shift, we found two different local susceptibilities which correspond to susceptibility of dimer and monomer spins, respectively. New field induced phase transition was found to occur at a critical field where the magnetic plateau onsets. A short range magnetic ordering developed in a peculiar two-stage process, which was revealed by temperature dependence of the magnetic specific heat and susceptibility.