Bogomyagkov, A.V. Druzhinin, V.P. Levichev, E.B. Milstein, A.I. Sinyatkin, S.V. JACoW Publishing Geneva, Switzerland From six leptonic atoms (e⁺e⁻), (μ+e-), (μ+μ-), (τ+e-), (τ+μ-), (τ+τ-) only positronium (e⁺e⁻) and muonium (μ+e-) were observed. Observation and study of dimuonium (μ+μ-) will test QED and quantum mechanics computations in the new regime. Dimuonium radius is 200 times smaller than positronium; therefore, it has a higher new-physics reach potential in comparison with other exotic atoms. We propose a low energy e⁺e⁻ collider for production of the not yet observed (μ+μ-) bound system. Low beam energy E(beam)=400 MeV and small circumference Π=30 m of the machine make it inexpensive to manufacture and operate. Large crossing angle (75 degrees)of e⁺e⁻ beams produces dimuonium with non-zero momentum shifting decay point from beams collision area and providing effective suppression of the main source of background – elastic e⁺e⁻ scattering. The peak luminosity at μ+μ- production threshold is 8×10³¹ cm⁻²s⁻¹. Reversing one of the beams direction allows to study π± and η mesons with high luminosity.