A protein complex composed of two identical immunoglobulin heavy chains of the IgM isotype and two identical immunoglobulin light chains, held together by disulfide bonds, and in its circulating form complexed with J chain in polymeric forms. An IgM immunoglobulin complex may be embedded in the plasma membrane or present in the extracellular space, in mucosal areas or other tissues, or circulating in the blood or lymph.