A file with the extension .ape, is an audio file compressed using Monkey's Audio. Monkey's Audio is a lossless compression, which means it does not permanently discard data during compression. It achieves compression rates of around 40%.
Since it is lossless, the quality of the audio after compression will be the exact same. There are several players for Monkey's Audio. One of the best is Foobar 2000.
I you need to burn Monkey's Audio as an Audio CD, you can do so with Nero Burning Rom if you download a plugin here.
Related software tools
Foobar 2000 (Freeware)
Foobar is an advanced audio player for audiophiles
Nero Burning ROM (Shareware)
Nero is the best and most complete DVDR / CDR / Blu-ray all-in-one software