Earth's Moon, lacking both a global magnetic field and any significant atmosphere, presents an ideal location to study plasma flow past a solar system body in one of its simplest incarnations. Despite its relative simplicity, however, the lunar wake interaction displays a rich array of physics, with both fluid and kinetic aspects. We present a new study of the lunar wake, using measurements from Lunar Prospector (LP) to determine the magnetic field, electron density and temperature, and electrostatic potential. We use these data and Wind key parameter data to characterize the wake near the Moon. At 85--115 km above the Moon we observe a classical wake signature, with enhanced magnetic fields in the central wake and reduced fields near the boundary. The magnetic signature at these altitudes responds clearly to changes in solar wind parameters, while that at 20--45 km depends mainly on crustal fields. We also observe an ambipolar potential drop across the wake boundary (resulting in central wake potentials of about -300 V relative to the solar wind) and greatly reduced electron density and increased electron temperature in the wake. The wake morphology, in terms of both electron parameters and magnetic fields, is well described by self-similar solutions for plasma expansion into a void and the resulting diamagnetic current system, but only if Kappa functions are used to describe the solar wind electron distributions.