FFmpeg
From MythTV Official Wiki
FFmpeg is a collection of free software that can record, convert and stream digital audio and video. It includes libavcodec (a leading audio/video codec library), and libavformat (a leading audio/video container mux and demux library). FFmpeg is developed under Linux, but it can be compiled under most operating systems, including Windows. [1]
Mythtv uses FFmpeg libraries Libavcodec, libavformat, and libavutil for its AV processing & displaying code, for example the internal player.