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F-Droid consists of both client and server software that enables people to easily install open source Android applications on their Android devices. The client is itself an Android application. The server component is a collection of "applications" that can be installed. The end-user experience is that of user friendly "app store" similar to the Google Play store or Apple App Store. Apps can also be downloaded from the F-Droid website and then installed manually. Applications can be installed from F-Droid without the need to register for an account.
Perhaps the most interesting aspect of F-Droid, is that is designed so that a user can "subscribe" to multiple sources (or app stores). F-Droid (the project) runs and hosts perhaps the largest collection of applications. These applications are strictly free software and make it clear which apps have "anti-features" such as advertising, user tracking, or dependence on non-free software aspects.
The Guardian Project runs an F-Droid store focused on security & privacy applications.