Mars' polar regions are covered with ice-rich layered deposits that potentially contain a record of climate variations. The sounding radar SHARAD on the Mars Reconnaissance Orbiter mapped detailed subsurface stratigraphy in the Promethei Lingula region of the south polar plateau, Planum Australe. Radar reflections interpreted as layers are correlated across adjacent orbits and are continuous for up to 150 kilometers along spacecraft orbital tracks. The reflectors are often separated into discrete reflector sequences, and strong echoes are seen as deep as 1 kilometer. In some cases, the sequences are dipping with respect to each other, suggesting an interdepositional period of erosion. In Australe Sulci, layers are exhumed, indicating recent erosion.