The Precision IceCube Next Generation Upgrade (PINGU) is a proposed low-energy in-fill extension to the IceCube Neutrino Observatory. With detection technology modeled closely on the successful IceCube example, PINGU will provide a 6 Mton effective mass for neutrino detection with an energy threshold of a few GeV. With an unprecedented sample of over 60 000 atmospheric neutrinos per year in this energy range, PINGU will make highly competitive measurements of neutrino oscillation parameters in an energy range over an order of magnitude higher than long-baseline neutrino beam experiments. PINGU will measure the mixing parameters theta(23) and Delta m(32)(2), including the octant of theta(23) for a wide range of values, and determine the neutrino mass ordering at 3 sigma median significance within five years of operation. PINGU's high precision measurement of the rate of nu(T) appearance will provide essential tests of the unitarity of the 3 x 3 PMNS neutrino mixing matrix. PINGU will also improve the sensitivity of searches for low mass dark matter in the Sun, use neutrino tomography to directly probe the composition of the Earth's core, and improve IceCube's sensitivity to neutrinos from Galactic supernovae. Reoptimization of the PINGU design has permitted substantial reduction in both cost and logistical requirements while delivering performance nearly identical to configurations previously studied.