The AAPS app (an apk file) is not available for download, due to regulations around medical devices. It is legal to build the app for your own use, but you must not give a copy to others!
See FAQ page for details.
Three methods are available to build the AAPS app:
You can build the app with your smartphone using GitHub actions, and save it in your Google Drive.
You can build the app with your computer using Android Studio. This used to be the only build option, nowadays Android Studio is mostly used by developers who consider making code changes.
This option is intended for those who prefer to build AAPS in local command-line, without installing Android Studio.