Applications of Perturbative NRQCD

We review the theoretical ideas and tools required to arrive at a next-to-next-to-leading order (NNLO) description of the heavy quark-antiquark production cross section in $e^+e^-$ annihilation for the case that the center of mass kinetic energy of the quarks is larger than $\Lambda_{QCD}$. In this case the NNLO cross section can be calculated with purely perturbative methods. We present details of the calculation and discuss two applications, the determination of the bottom quark mass from Upsilon sum rules and the top-antitop production cross section close to threshold in $e^+e^-$ annihilation.