From Hydrogenaudio Knowledgebase
Monkey's Audio (APE) is a free lossless audio compression format with a highly competitive compression algorithm, and is used primarily by Windows users. Although software is available for Linux, Monkey's Audio is not as popular among this operating system's users. Monkey's Audio suffers from slow decompression speeds as compared to other lossless audio codecs.
Monkey's Audio uses a combination of traditional lossless compression tactics (linear prediction and channel coupling) and a simple Neural network. To store the output values of its prediction step it uses Range coding, modified to work well with more or less continuous values.
Monkey's Audio's main competitor is FLAC, which has more features than Monkey's Audio (streaming support, for example) and hardware support to its advantage, though its efficiency in compression is not as great.
Monkey's Audio is released under a "custom" license that allows you to do pretty much anything with the source code, on the provision that you ask the author for permission.