  We present the analytic total cross section of top quark pair production in
electron-positron annihilation at next-to-next-to-leading order (NNLO) in
Quantum Chromodynamics (QCD). By utilizing the optical theorem, the NNLO
corrections are related to the imaginary parts of three-loop self-energy
Feynman diagrams, of which the master integrals are calculated with canonical
differential equations. The analytic results for the NNLO corrections are
expressed in terms of multiple polylogarithms as well as elliptic functions. We
discuss the asymptotic expansions near the threshold and in the high energy
limit in detail. Numerical results are provided for the total cross section of
top quark pair production at future lepton colliders.
