Production of $(τ^+τ^-)_b$ in electron positron collisions
$(τ^+τ^-)_b$ is an atom of simple hydrogenlike structure similar to positronium $(e^+e^-)_b$ and $(μ^+μ^-)_b$. In this paper energy levels and decay widths of different decay channels of $(τ^+τ^-)_b$ are given. Cross section of production of this atomic system in $e^+e^-$ annihilation taking into account radiative corrections is calculated. According to our estimates 886 $(τ^+τ^-)_b$ atoms may be produced at BEPCII and 29 $(τ^+τ^-)_b$ atoms are produced at VEPP-4M under the present experimental conditions.