This paper motivates and describes GALE, the Generic Adaptation Language and Engine that came out of the GRAPPLE EU FP7 project. The main focus of the paper is the extensible nature of GALE. The purpose of this description is to illustrate how a single core adaptation engine can be used for different types of adaptation, applied to different types of information items and documents. We illustrate the adaptive functionality on some examples of hypermedia documents. In April 2012, David Smits defended the world's first adaptive PhD thesis on this topic. The thesis, available for download and direct adaptive access at http://gale.win.tue.nl/thesis/, shows that a single source of information can serve different audiences and at the same time also allows more freedom of navigation than is possible in any paper or static hypermedia document. The same can be done for course texts, hyperfiction, encyclopedia, museum, or other cultural heritage websites, etc. We explain how to add functionality to GALE if desired, to adapt the system's behavior to whatever the application requires. This stresses our main objective: to provide a technological base for adaptive (hypermedia) system researchers on which they can build extensions for the specific research they have in mind.